Module-valued functors preserving the covering dimension

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F44555601%3A13440%2F15%3A43886683" target="_blank" >RIV/44555601:13440/15:43886683 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.14712/1213-7243.2015.131" target="_blank" >http://dx.doi.org/10.14712/1213-7243.2015.131</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2015.131" target="_blank" >10.14712/1213-7243.2015.131</a>

Result language
angličtina
Original language name
Module-valued functors preserving the covering dimension
Original language description
We prove a general theorem about preservation of the covering dimension $dim$ by certain covariant functors that implies, among others, the following concrete results: (i) If $G$ is a pathwise connected separable metric NSS abelian group and $X$, $Y$ are Tychonoff spaces such that the group-valued function spaces $C_p(X,G)$ and $C_p(Y,G)$ are topologically isomorphic as topological groups, hen $dim X=dim Y$. (ii) If free precompact abelian groups of Tychonoff spaces $X$ are $Y$ are topologically isomorphic, then $dim X=dim Y$. (iii) If $R$ is a topological ring with a countable network and the free topological $R$-modules of Tychonoff spaces $X$ and $Y$ are topologically isomorphic, then $dim X=dim Y$. The classical result of Pestov - [V.G. Pestov, The coincidence of the dimensions dim of l-equivalent spaces,} Soviet Math.Dokl. textbf{26} (1982) No.2, 380-383.] about preservation of the covering dimension by $l$-equivalence immediately follows from item (i) by taking the topolo
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GPP201%2F12%2FP724" target="_blank" >GPP201/12/P724: Relations between topological spaces and their topological groups of G-valued continuous functions for a given topological group G</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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