Approximation by light maps and parametric Lelek maps
| dc.creator | Banakh, Taras | |
| dc.creator | Valov, Vesko | |
| dc.date | 2008-01-20 | |
| dc.date.accessioned | 2026-07-07T08:55:36Z | |
| dc.date.available | 2026-07-07T08:55:36Z | |
| dc.description | The 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.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0801.3107 | |
| dc.identifier | http://arxiv.org/abs/0801.3107 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146321 | |
| dc.subject | Geometric Topology | |
| dc.subject | General Topology | |
| dc.subject | 54F45 (Primary); 55M10(Secondary) | |
| dc.title | Approximation by light maps and parametric Lelek maps | |
| dc.type | text |