# Module-valued functors preserving the covering dimension

Commentationes Mathematicae Universitatis Carolinae (2015)

- Volume: 56, Issue: 3, page 377-399
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top-
If

$G$ is a pathwise connected separable metric NSS abelian group andG $X$ ,X $Y$ are Tychonoff spaces such that the group-valued function spacesY ${C}_{p}(X,G)$ andC_p(X,G) ${C}_{p}(Y,G)$ are topologically isomorphic as topological groups, thenC_p(Y,G) $dimX=dimY$ .\operatorname{dim} X=\operatorname{dim} Y -
If free precompact abelian groups of Tychonoff spaces

$X$ andX $Y$ are topologically isomorphic, thenY $dimX=dimY$ .\operatorname{dim} X=\operatorname{dim} Y -
If

$R$ is a topological ring with a countable network and the free topologicalR $R$ -modules of Tychonoff spacesR $X$ andX $Y$ are topologically isomorphic, thenY $dimX=dimY$ .\operatorname{dim} X=\operatorname{dim} Y

## How to cite

topSpěvák, Jan. "Module-valued functors preserving the covering dimension." Commentationes Mathematicae Universitatis Carolinae 56.3 (2015): 377-399. <http://eudml.org/doc/271625>.

@article{Spěvák2015,

abstract = {We prove a general theorem about preservation of the covering dimension $\operatorname\{dim\}$ by certain covariant functors that implies, among others, the following concrete results.
The classical result of Pestov [The coincidence of the dimensions dim of $l$-equivalent spaces, Soviet Math. Dokl. 26 (1982), no. 2, 380–383] about preservation of the covering dimension by $l$-equivalence immediately follows from item (i) by taking the topological group of real numbers as $G$.},

author = {Spěvák, Jan},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {covering dimension; topological group; function space; topology of pointwise convergence; free topological module; $l$-equivalence; $G$-equivalence},

language = {eng},

number = {3},

pages = {377-399},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Module-valued functors preserving the covering dimension},

url = {http://eudml.org/doc/271625},

volume = {56},

year = {2015},

}

TY - JOUR

AU - Spěvák, Jan

TI - Module-valued functors preserving the covering dimension

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2015

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 56

IS - 3

SP - 377

EP - 399

AB - We prove a general theorem about preservation of the covering dimension $\operatorname{dim}$ by certain covariant functors that implies, among others, the following concrete results.
The classical result of Pestov [The coincidence of the dimensions dim of $l$-equivalent spaces, Soviet Math. Dokl. 26 (1982), no. 2, 380–383] about preservation of the covering dimension by $l$-equivalence immediately follows from item (i) by taking the topological group of real numbers as $G$.

LA - eng

KW - covering dimension; topological group; function space; topology of pointwise convergence; free topological module; $l$-equivalence; $G$-equivalence

UR - http://eudml.org/doc/271625

ER -

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