Approximation by light maps and parametric Lelek maps

dc.creatorBanakh, Taras
dc.creatorValov, Vesko
dc.date2008-01-20
dc.date.accessioned2026-07-07T08:55:36Z
dc.date.available2026-07-07T08:55:36Z
dc.descriptionThe class of metrizable spaces $M$ with the following approximation property is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is $\e$-homotopic to $g$. It is shown that this class has very nice properties. For example, if $M_i\in AP(n_i,0)$, $i=1,2$, then $M_1\times M_2\in AP(n_1+n_2,0)$. Moreover, $M\in AP(n,0)$ if and only if each point of $M$ has a local base of neighborhoods $U$ with $U\in AP(n,0)$. Using the properties of AP(n,0)-spaces, we generalize some results of Levin and Kato-Matsuhashi concerning the existence of residual sets of $n$-dimensional Lelek maps.
dc.description34 pages
dc.identifierhttps://arxiv.org/abs/0801.3107
dc.identifierhttp://arxiv.org/abs/0801.3107
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146321
dc.subjectGeometric Topology
dc.subjectGeneral Topology
dc.subject54F45 (Primary); 55M10(Secondary)
dc.titleApproximation by light maps and parametric Lelek maps
dc.typetext

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