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Cohomological dimension of Tychonov spaces
Abstract The concept of the cohomological dimension dim G X is defined for any Tychonov (i.e., completely regular and Hausdorff) space X and any countable abelian group G . We prove that dim G X =Expand
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Which compacta are noncommutative ARs
We give a short answer to the question in the title: {\em dendrits}. Precisely we show that the $C^{\ast}$-algebra $C(X)$ of all complex-valued continuous functions on a compactum $X$ is projectiveExpand
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The theory of n-shapes
CONTENTS Introduction § 1. n-homotopy § 2. n-shape § 3. n-shape and UVn-maps § 4. n-cohomology groups § 5. n-homology and n-homotopy groups References
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On a generalization of perfectly normal spaces
Abstract The notion of quasi-perfect normality which generalizes the notion of usual perfect normality is introduced and the behavior of the dimension functions in this class of spaces isExpand
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Compactifications and universal spaces in extension theory
We show that for each countable simplicial complex P the following conditions are equivalent: (1) $P \in AE(X)$ iff $P \in AE(\beta X)$ for any space X; (2) There exists a P-invertible map of aExpand
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Infinite Dimensional Topology and Shape Theory
Infinite dimensional topology, in its traditional understanding, is a branch of geometric topology which studies infinite dimensional spaces, arising naturally in topology and functional analysis.Expand
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COMPACTA LYING IN THE $ n$-DIMENSIONAL UNIVERSAL MENGER COMPACTUM AND HAVING HOMEOMORPHIC COMPLEMENTS IN IT
The concept of -shape is defined for an arbitrary compactum, and it is proved that two -sets lying in the -dimensional universal Menger compactum have homeomorphic complements in it precisely whenExpand
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COMPACT GROUPS AND FIXED POINT SETS
Some structure theorems for compact abelian groups are derived and used to show that every closed subset of an infinite compact metrizable group is the fixed point set of an autohomeomorphism. It isExpand
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Approximations and Selections of Multivalued Mappings of Finite-Dimensional Spaces
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
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On bicompact extensions of tychonoff spaces
Necessary and sufficient conditions for existence of the minimal elements in some subsets of the partially-ordered set of all Hausdorff bicompact extensions of the completely regularT1 spaces areExpand
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