Extension dimensional approximation theorem
| dc.creator | Brodsky, N. | |
| dc.creator | Chigogidze, A. | |
| dc.date | 2001-03-09 | |
| dc.date | 2001-09-22 | |
| dc.date.accessioned | 2026-07-07T04:40:34Z | |
| dc.date.available | 2026-07-07T04:40:34Z | |
| dc.description | Let $L$ be a countable CW-complex and $F\colon X\to Y$ be upper semicontinuous $UV^{[L]}$-valued mapping of a paracompact space $X$ to a complete metric space $Y$. We prove that if $X$ is a C-space of extension dimension $\ed X \le [L]$, then $F$ admits single-valued graph approximations. For $L=S^n$ our result implies well-known approximation theorem for $UV^{n-1}$-valued mappings of $n$-dimensional spaces. And for $L=\{\rm point\}$ our theorem implies a theorem of Ancel on approximations of $UV^\infty$-valued mappings of C-spaces. | |
| dc.description | 7 pages, final version, minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0103061 | |
| dc.identifier | http://arxiv.org/abs/math/0103061 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61068 | |
| dc.subject | General Topology | |
| dc.subject | 54C65 | |
| dc.title | Extension dimensional approximation theorem | |
| dc.type | text |