Contact algebra is one of the main tools in region-based theory of space. In it is generalized by dropping the operation Boolean complement. Furthermore we can generalize contact algebra by dropping also the operation meet. Thus we obtain structures, called contact join-semilattices and structures, called distributive contact join-semilattices. We obtain a set-theoretical representation theorem for CJS and a relational representation theorem for DCJS. As corollaries we get also topological representation theorems. We prove that the universal theory of CJS and of (...) DCJS is the same and is decidable. (shrink)

The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C, called contact. Standard models of contact algebras are topological and are the contact algebras of regular closed sets in a given topological space. In such a contact algebra we add the predicate of internal connectedness with the following meaning—a regular closed set is internally connected if and only if its interior is (...) a connected topological space in the subspace topology. We add also a ternary relation \ meaning that the intersection of the first two arguments is included in the third. In this paper the extension of a Boolean algebra with \, contact and internal connectedness, satisfying certain axioms, is called an extended contact algebra. We prove a representation theorem for extended contact algebras and thus obtain an axiomatization of the theory, consisting of the universal formulas, true in all topological contact algebras with added relations of internal connectedness and \. (shrink)

The coronavirus disease 2019 not only will have negative impacts on religious beliefs, but will also deepen them. Attention to Islamic teachings is significantly important in dealing with the COVID-19 pandemic. Nevertheless, the increased outbreak of COVID-19 in the world shows the need for humanity to pay more attention to religion and theology. Islam prevents diseases and motivates people to adhere to hygiene principles, and Islamic teachings bring about purity and health to people. However, paying attention to God, chanting prayers (...) and focusing on spirituality are key principles in the prevention and treatment of diseases as this material cause is the divine will. Everyone is under the power of the Almighty, and everything is in his hands. Nevertheless, human beings may pass away because of COVID-19 even after passing all these stages. This is, however, related to divine destiny and is beyond the aim of this research study. One of the issues that relate religion to COVID-19 is psychological resilience, which is the topic of this study. This research study aimed at evaluating the role of religion and religiosity in the psychological resilience of 550 Muslim citizens from three cities of Aceh, Semarang and Jakarta, who had recovered from COVID-19. We applied the convenience sampling method to determine the sample size. After the distribution of questionnaires, 536 tools were considered suitable, and data analysis was performed using mean and correlation tests. According to the results, religiosity affected psychological resilience by p = 0.784.Contribution: The results of this study revealed that with increasing attention of people to religious teachings, the psychological resilience to the COVID-19 also increases. (shrink)

In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free (...) and point-based models of space in terms of extended contact. More precisely, we prove new representation theorems for extended contact algebras. (shrink)