Connectivity properties of dimension level sets

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Mathematical Logic Quarterly 54 (5):483-491 (2008)
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Abstract

This paper initiates the study of sets in Euclidean spaces ℝn that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, n ], we are interested in the connectivity properties of the set DIMI, consisting of all points in ℝn whose dimensions lie in I, and of its dual DIMIstr, consisting of all points whose strong dimensions lie in I. If I is [0, 1) or

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10.1002/malq.200710060

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Citations of this work

Completeness, Compactness, Effective Dimensions.Stephen Binns - 2013 - Mathematical Logic Quarterly 59 (3):206-218.

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Von Mises' definition of random sequences reconsidered.Michiel van Lambalgen - 1987 - Journal of Symbolic Logic 52 (3):725-755.

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