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Cohomological dimension of Tychonov spaces

- A. Chigogidze
- Mathematics
- 16 September 1997

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

- A. Chigogidze, A. Dranishnikov
- Mathematics
- 17 February 2009

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 projective… Expand

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The theory of n-shapes

- A. Chigogidze
- Mathematics
- 31 October 1989

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

24 2

On a generalization of perfectly normal spaces

- A. Chigogidze
- Mathematics
- 1982

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 is… Expand

14 2

Compactifications and universal spaces in extension theory

- A. Chigogidze
- Mathematics
- 15 August 1999

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 a… Expand

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Infinite Dimensional Topology and Shape Theory

- A. Chigogidze
- Mathematics
- 2001

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

29 2

COMPACTA LYING IN THE $ n$-DIMENSIONAL UNIVERSAL MENGER COMPACTUM AND HAVING HOMEOMORPHIC COMPLEMENTS IN IT

- A. Chigogidze
- Mathematics
- 28 February 1988

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 when… Expand

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COMPACT GROUPS AND FIXED POINT SETS

- A. Chigogidze, K. Hofmann, J. Martin
- Mathematics
- 1997

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 is… Expand

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Approximations and Selections of Multivalued Mappings of Finite-Dimensional Spaces

- N. Brodsky, A. Chigogidze, A. Karasev
- Mathematics
- 9 June 2001

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

9 1

On bicompact extensions of tychonoff spaces

- A. Chigogidze
- Mathematics
- 1 September 1979

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 are… Expand

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