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December 2004 On universality of finite products of Polish spaces
T. Banakh, R. Cauty, K. Trushchak, L. Zdomsky
Tsukuba J. Math. 28(2): 455-471 (December 2004). DOI: 10.21099/tkbjm/1496164811


We introduce and study the $n$-Dimensional Perfect Homotopy Approximation Property (briefly $n$-PHAP) equivalent to the discrete $n$-cells property in the realm of $LC^{n}$-spaces. It is shown that the product $X\times Y$ of a space $X$ with $n$-PHAP and a space $Y$ with $m$-PHAP has $(n+m+1)$-PHAP. We derive from this that for a (nowhere locally compact) locally connected Polish space $X$ without free arcs and for each $n\geq 0$ the power $X^{n+1}$ contains a closed topological copy of each at most $n$-dimensional compact (resp. Polish) space.


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T. Banakh. R. Cauty. K. Trushchak. L. Zdomsky. "On universality of finite products of Polish spaces." Tsukuba J. Math. 28 (2) 455 - 471, December 2004.


Published: December 2004
First available in Project Euclid: 30 May 2017

zbMATH: 1131.57024
MathSciNet: MR2105947
Digital Object Identifier: 10.21099/tkbjm/1496164811

Rights: Copyright © 2004 University of Tsukuba, Institute of Mathematics


Vol.28 • No. 2 • December 2004
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