Results for 'Topological space'

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  1. Topological space as a model of being in the late working notes of Maurice Merleau-Ponty.Martin Nitsche - 2010 - Filosoficky Casopis 58 (1):49-56.
     
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  2. Modal Logics for Topological Spaces.Konstantinos Georgatos - 1993 - Dissertation, City University of New York
    In this thesis we present two logical systems, $\bf MP$ and $\MP$, for the purpose of reasoning about knowledge and effort. These logical systems will be interpreted in a spatial context and therefore, the abstract concepts of knowledge and effort will be defined by concrete mathematical concepts.
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  3.  18
    Effective topological spaces II: A hierarchy.Iraj Kalantari & Galen Weitkamp - 1985 - Annals of Pure and Applied Logic 29 (2):207-224.
    This paper is an investigation of definability hierarchies on effective topological spaces. An open subset U of an effective space X is definable iff there is a parameter free definition φ of U so that the atomic predicate symbols of φ are recursively open relations on X . The complexity of a definable open set may be identified with the quantifier complexity of its definition. For example, a set U is an ∃∃∀∃-set if it has an ∃∃∀∃ parameter (...)
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  4. On topological spaces equivalent to ordinals.Jörg Flum & Juan Carlos Martinez - 1988 - Journal of Symbolic Logic 53 (3):785-795.
    Let L be one of the topological languages L t , (L ∞ω ) t and (L κω ) t . We characterize the topological spaces which are models of the L-theory of the class of ordinals equipped with the order topology. The results show that the role played in classical model theory by the property of being well-ordered is taken over in the topological context by the property of being locally compact and scattered.
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  5.  7
    Knowledge Theoretic Properties of Topological Spaces.Konstantinos Georgatos - 1994 - In Masuch, Michael & Polos Laszlo (eds.), Knowledge Representation and Uncertainty. Springer Verlag. pp. 147--159.
    We study the topological models of a logic of knowledge for topological reasoning, introduced by Larry Moss and Rohit Parikh (1992). Among our results is the confirmation of a conjecture by Moss and Parikh, as well as the finite satisfiability property and decidability for the theory of topological models.
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  6.  35
    Announcement as effort on topological spaces.Hans van Ditmarsch, Sophia Knight & Aybüke Özgün - 2019 - Synthese 196 (7):2927-2969.
    We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and (...)
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  7.  6
    Announcement as effort on topological spaces.Aybüke Özgün, Sophia Knight & Hans Ditmarsch - 2019 - Synthese 196 (7):2927-2969.
    We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and (...)
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  8.  11
    Effective topological spaces I: A definability theory.Iraj Kalantari & Galen Weitkamp - 1985 - Annals of Pure and Applied Logic 29 (1):1-27.
  9.  7
    Effective topological spaces III: Forcing and definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36:17-27.
  10. On effective topological spaces.Dieter Spreen - 1998 - Journal of Symbolic Logic 63 (1):185-221.
    Starting with D. Scott's work on the mathematical foundations of programming language semantics, interest in topology has grown up in theoretical computer science, under the slogan `open sets are semidecidable properties'. But whereas on effectively given Scott domains all such properties are also open, this is no longer true in general. In this paper a characterization of effectively given topological spaces is presented that says which semidecidable sets are open. This result has important consequences. Not only follows the classical (...)
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  11.  23
    Disjoint Unions of Topological Spaces and Choice.Paul Howard, Kyriakos Keremedis, Herman Rubin & Jean E. Rubin - 1998 - Mathematical Logic Quarterly 44 (4):493-508.
    We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.
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  12.  10
    Normal Domain Representations of Topological Spaces.Ivar Rummelhoff - 2001 - Mathematical Logic Quarterly 47 (3):409-412.
    D′ ⊆ D is a normal totality on a Scott domain D if it is upward closed and x ⊓ y ∈ D′ is an equivalence relation on D′. We prove that every topological space can be represented by a domain with norma totality.
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  13.  15
    Recursive constructions in topological spaces.Iraj Kalantari & Allen Retzlaff - 1979 - Journal of Symbolic Logic 44 (4):609-625.
    We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological space X. Various constructions produce complemented recursively enumerable open sets with additional recursion theoretic properties, as well as noncomplemented open sets. In contrast to techniques in classical topology, we construct a disjoint recursively enumerable collection of basic open sets which cannot be extended to a recursively enumerable disjoint collection of basic open sets whose union is dense in (...)
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  14.  13
    Point-free topological spaces, functions and recursive points; filter foundation for recursive analysis. I.Iraj Kalantari & Lawrence Welch - 1998 - Annals of Pure and Applied Logic 93 (1-3):125-151.
    In this paper we develop a point-free approach to the study of topological spaces and functions on them, establish platforms for both and present some findings on recursive points. In the first sections of the paper, we obtain conditions under which our approach leads to the generation of ideal objects with which mathematicians work. Next, we apply the effective version of our approach to the real numbers, and make exact connections to the classical approach to recursive reals. In the (...)
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  15.  18
    Degrees of recursively enumerable topological spaces.Iraj Kalantari & J. B. Remmel - 1983 - Journal of Symbolic Logic 48 (3):610-622.
    In [5], Metakides and Nerode introduced the study of recursively enumerable substructures of a recursively presented structure. The main line of study presented in [5] is to examine the effective content of certain algebraic structures. In [6], Metakides and Nerode studied the lattice of r.e. subspaces of a recursively presented vector space. This lattice was later studied by Kalantari, Remmel, Retzlaff and Shore. Similar studies have been done by Metakides and Nerode [7] for algebraically closed fields, by Remmel [10] (...)
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  16. Squares of Oppositions, Commutative Diagrams, and Galois Connections for Topological Spaces and Similarity Structures.Thomas Mormann - manuscript
    The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.
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  17.  2
    Pseudointersection numbers, ideal slaloms, topological spaces, and cardinal inequalities.Jaroslav Šupina - 2023 - Archive for Mathematical Logic 62 (1):87-112.
    We investigate several ideal versions of the pseudointersection number \(\mathfrak {p}\), ideal slalom numbers, and associated topological spaces with the focus on selection principles. However, it turns out that well-known pseudointersection invariant \(\mathtt {cov}^*({\mathcal I})\) has a crucial influence on the studied notions. For an invariant \(\mathfrak {p}_\mathrm {K}({\mathcal J})\) introduced by Borodulin-Nadzieja and Farkas (Arch. Math. Logic 51:187–202, 2012), and an invariant \(\mathfrak {p}_\mathrm {K}({\mathcal I},{\mathcal J})\) introduced by Repický (Real Anal. Exchange 46:367–394, 2021), we have $$\begin{aligned} \min (...)
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  18.  10
    Private Announcements on Topological Spaces.Aybüke Özgün, Sophia Knight & Hans Ditmarsch - 2018 - Studia Logica 106 (3):481-513.
    In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information $$\varphi $$ φ, while all the other agents observe that group G is informed, but are uncertain whether the information provided is $$\varphi $$ φ or $$\lnot \varphi $$ ¬φ. This article follows up on our prior work where the dynamics (...)
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  19.  25
    Private Announcements on Topological Spaces.Hans van Ditmarsch, Sophia Knight & Aybüke Özgün - 2018 - Studia Logica 106 (3):481-513.
    In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information \, while all the other agents observe that group G is informed, but are uncertain whether the information provided is \ or \. This article follows up on our prior work where the dynamics were public events. We provide a complete (...)
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  20.  8
    Interval Valued Neutrosophic Soft Topological Spaces.Anjan Mukherjee, Mithun Datta & Florentin Smarandache - 2014 - Neutrosophic Sets and Systems 6:18-27.
    In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology. We also define interval valued neutrosophic interior and closer of an interval valued neutrosophic soft set. Some theorems and examples are cites. Interval valued neutrosophic soft subspace topology are studied. Some examples and theorems regarding this concept are presented.
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  21.  12
    Categories of Topological Spaces and Scattered Theories.R. W. Knight - 2007 - Notre Dame Journal of Formal Logic 48 (1):53-77.
    We offer a topological treatment of scattered theories intended to help to explain the parallelism between, on the one hand, the theorems provable using Descriptive Set Theory by analysis of the space of countable models and, on the other, those provable by studying a tree of theories in a hierarchy of fragments of infinintary logic. We state some theorems which are, we hope, a step on the road to fully understanding counterexamples to Vaught's Conjecture. This framework is in (...)
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  22.  9
    Completions, comonoids, and topological spaces.Anna Bucalo & Giuseppe Rosolini - 2006 - Annals of Pure and Applied Logic 137 (1-3):104-125.
    We analyse the category-theoretical structures involved with the notion of continuity within the framework of formal topology. We compare the category of basic pairs to other categories of “spaces” by means of canonically determined functors and show how the definition of continuity is determined in a certain, canonical sense. Finally, we prove a standard adjunction between the algebraic approach to spaces and the category of topological spaces.
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  23.  8
    Dynamical algebraic structures, pointfree topological spaces and Hilbert's program.Henri Lombardi - 2006 - Annals of Pure and Applied Logic 137 (1-3):256-290.
  24.  37
    Double enlargements of topological spaces.Paul Goodyear - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (25):389-392.
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  25.  39
    Corrigendum: On effective topological spaces.Dieter Spreen - 2000 - Journal of Symbolic Logic 65 (4):1917-1918.
  26.  10
    Finitely Additive Measures on Topological Spaces and Boolean Algebras, University of East Anglia, UK, 2015. Supervised by Mirna Džamonja.Zanyar A. Ameen & Mirna Džamonja - 2018 - Bulletin of Symbolic Logic 24 (2):199-200.
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  27.  10
    A linearly ordered topological space that is not normal.Melven Krom - 1986 - Notre Dame Journal of Formal Logic 27 (1):12-13.
  28.  47
    Near orderings of topological spaces.Terry D. Lenker & Richard St André - 1983 - Synthese 55 (3):327 - 331.
  29.  60
    Some Results on Modal Axiomatization and Definability for Topological Spaces.Guram Bezhanishvili, Leo Esakia & David Gabelaia - 2005 - Studia Logica 81 (3):325-355.
    We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the (...)
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  30.  27
    Review: Andrzej Grzegorczyk, Some Relational Systems and the Associated Topological Spaces. [REVIEW]R. A. Bull - 1969 - Journal of Symbolic Logic 34 (4):652-653.
  31.  9
    Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces.A. A. Salama, Florentin Smarandache & Valeri Kroumov - 2014 - Neutrosophic Sets and Systems 2:25-30.
    In this paper, we generalize the crisp topological spaces to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology.
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  32. The impossibility of relations between non-collocated spatial objects and non-identical topological spaces.Jeffrey Grupp - 2005 - Axiomathes 15 (1):85-141.
    I argue that relations between non-collocated spatial entities, between non-identical topological spaces, and between non-identical basic building blocks of space, do not exist. If any spatially located entities are not at the same spatial location, or if any topological spaces or basic building blocks of space are non-identical, I will argue that there are no relations between or among them. The arguments I present are arguments that I have not seen in the literature.
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  33.  14
    Chainable and circularly chainable semicomputable sets in computable topological spaces.Eugen Čičković, Zvonko Iljazović & Lucija Validžić - 2019 - Archive for Mathematical Logic 58 (7-8):885-897.
    We examine conditions under which, in a computable topological space, a semicomputable set is computable. It is known that in a computable metric space a semicomputable set S is computable if S is a continuum chainable from a to b, where a and b are computable points, or S is a circularly chainable continuum which is not chainable. We prove that this result holds in any computable topological space.
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  34.  13
    René Thom, Reader of Jakob von Uexküll (Meaning as Topological Space).Arthur Araujo - 2022 - Biosemiotics 15 (3):555-573.
    In this paper, I draw a parallel between aspects of René Thom’s topological program understood as semiophysics, and Jakob von Uexküll’s theory of meaning. Through the use of Thom’s semiophysics, I believe that it is possible to interpret Uexküll’s intuition that meaning unfolds a kind of transformation in an organism’s transactions with the environment: that is, meaning incorporates topological spaces. The central idea in question is that beyond the semantic, syntactical and pragmatic human use of language, meaning incorporates (...)
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  35.  25
    Completeness of public announcement logic in topological spaces.C. A. N. Baskent - 2011 - Bulletin of Symbolic Logic 17 (1):142.
  36.  4
    Frigyes Riesz and the emergence of general topology: The roots of ‘topological space’ in geometry.Laura Rodríguez - 2015 - Archive for History of Exact Sciences 69 (1):55-102.
    In 1906, Frigyes Riesz introduced a preliminary version of the notion of a topological space. He called it a mathematical continuum. This development can be traced back to the end of 1904 when, genuinely interested in taking up Hilbert’s foundations of geometry from 1902, Riesz aimed to extend Hilbert’s notion of a two-dimensional manifold to the three-dimensional case. Starting with the plane as an abstract point-set, Hilbert had postulated the existence of a system of neighbourhoods, thereby introducing the (...)
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  37.  15
    The undecidability of the lattice of R.E. closed subsets of an effective topological space.Sheryl Silibovsky Brady & Jeffrey B. Remmel - 1987 - Annals of Pure and Applied Logic 35 (C):193-203.
    The first-order theory of the lattice of recursively enumerable closed subsets of an effective topological space is proved undecidable using the undecidability of the first-order theory of the lattice of recursively enumerable sets. In particular, the first-order theory of the lattice of recursively enumerable closed subsets of Euclidean n -space, for all n , is undecidable. A more direct proof of the undecidability of the lattice of recursively enumerable closed subsets of Euclidean n -space, n ⩾ (...)
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  38.  22
    Some Relational Systems and the Associated Topological Spaces.Andrzej Grzegorczyk - 1969 - Journal of Symbolic Logic 34 (4):652-653.
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  39.  34
    Filters, Antichains and Towers in Topological Spaces and the Axiom of Choice.Kyriakos Keremedis - 1998 - Mathematical Logic Quarterly 44 (3):359-366.
    We find some characterizations of the Axiom of Choice in terms of certain families of open sets in T1 spaces.
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  40.  22
    Nonconstructive Properties of Well-Ordered T 2 topological Spaces.Kyriakos Keremedis & Eleftherios Tachtsis - 1999 - Notre Dame Journal of Formal Logic 40 (4):548-553.
    We show that none of the following statements is provable in Zermelo-Fraenkel set theory (ZF) answering the corresponding open questions from Brunner in ``The axiom of choice in topology'':(i) For every T2 topological space (X, T) if X is well-ordered, then X has a well-ordered base,(ii) For every T2 topological space (X, T), if X is well-ordered, then there exists a function f : X × W T such that W is a well-ordered set and f (...)
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  41.  1
    Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces.Xiongwei Zhang, Ibtesam Alshammari & A. Ghareeb - 2021 - Complexity 2021:1-7.
    Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the (...)
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  42.  21
    Andrzej Grzegorczyk. Some relational systems and the associated topological spaces. Fundamenta mathematicae, vol. 60 , pp. 223–231. [REVIEW]R. A. Bull - 1969 - Journal of Symbolic Logic 34 (4):652-653.
  43.  31
    Martin's axiom and a regular topological space with uncountable net weight whose countable product is hereditarily separable and hereditarily lindelöf.Krzysztof Ciesielski - 1987 - Journal of Symbolic Logic 52 (2):396-399.
  44.  9
    A. V. Arkhangel′skiĭ. O moshchnosti bikompaktov c pervoĭ aksiomoĭ schetnosti. Dok-lady Akademii Nauk SSSR, vol. 187 , pp. 967–970. - A. V. Arhangel′skiĭ. On the cardinality of bicompacta satisfying the first axiom of countability. English translation by Z. Skalsky of the preceding. Soviet mathematics, vol. 10 , pp. 951–955. - R. Pol. Short proofs of two theorems on cardinality of topological spaces. English with Russian summary. Bulletin de l'Académie Polonaise des Sciences Série des sciences mathématiques, astronomique et physiques, vol. 22 , pp. 1245–1249. - Alan Dow. An introduction to applications of elementary submodels to topology. Topology proceedings , vol. 13 , pp. 17–72. [REVIEW]Zoltan T. Balogh - 2001 - Bulletin of Symbolic Logic 7 (4):537-537.
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  45. Resolution Spaces: A Topological Approach to Similarity.Konstantinos Georgatos - 2000 - In DEXA 2000. IEEE Computer Society. pp. 553-557.
    A central concept for information retrieval is that of similarity. Although an information retrieval system is expected to return a set of documents most relevant to the query word(s), it is often described as returning a set of documents most similar to the query. The authors argue that in order to reason with similarity we need to model the concept of discriminating power. They offer a simple topological notion called resolution space that provides a rich mathematical framework for (...)
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  46.  4
    Topological Subset Space Models for Public Announcements.Adam Bjorndahl - 2018 - In Hans van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Springer. pp. 165-186.
    We reformulate a key definition given by Wáng and Ågotnes to provide semantics for public announcements in subset spaces. More precisely, we interpret the precondition for a public announcement of ???? to be the “local truth” of ????, semantically rendered via an interior operator. This is closely related to the notion of ???? being “knowable”. We argue that these revised semantics improve on the original and offer several motivating examples to this effect. A key insight that emerges is the crucial (...)
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  47.  14
    Space-time topology and quantum gravity.John L. Friedman - 1991 - In A. Ashtekar & J. Stachel (eds.), Conceptual Problems of Quantum Gravity. Birkhauser. pp. 1--539.
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  48.  9
    Cardinal spaces and topological representations of bimodal logics.Benedikt Löwe & Darko Sarenac - 2005 - Logic Journal of the IGPL 13 (3):301-306.
    We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.
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  49.  20
    Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points.Natasha Dobrinen, José G. Mijares & Timothy Trujillo - 2017 - Archive for Mathematical Logic 56 (7-8):733-782.
    A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing (...)
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  50. Topology Change and the Unity of Space.Craig Callender & Robert Weingard - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (2):227-246.
    Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical (...)
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