Extension dimension for paracompact spaces
| dc.creator | Dydak, Jerzy | |
| dc.date | 2002-10-28 | |
| dc.date.accessioned | 2026-07-07T09:23:23Z | |
| dc.date.available | 2026-07-07T09:23:23Z | |
| dc.description | We prove existence of extension dimension for paracompact spaces. Here is the main result of the paper: \proclaim{Theorem} Suppose X is a paracompact space. There is a CW complex K such that {a.} K is an absolute extensor of X up to homotopy, {b.} If a CW complex L is an absolute extensor of X up to homotopy, then L is an absolute extensor of Y up to homotopy of any paracompact space Y such that K is an absolute extensor of Y up to homotopy. proclaim The proof is based on the following simple result (see 1.6). \proclaim{Theorem} Suppose X be a paracompact space and $f:A\to Y$ is a map from a closed subset A of X to a space Y. f extends over X if Y is the union of a family $\{Y_s\}_{s\in S}$ of its subspaces with the following properties: {a.} Each $Y_s$ is an absolute extensor of X, {b.} For any two elements s and t of S there is $u\in S$ such that $Y_s\cup Y_t\subset Y_u$, {c.} $A=\bigcup\limits_{s\in S} \int_A(f^{-1}(Y_s))$. proclaim That result implies a few well-known theorems of classical theory of retracts which makes it of interest in its own. | |
| dc.description | 17 pages, to appear in Topology and its Applications | |
| dc.identifier | https://arxiv.org/abs/math/0210424 | |
| dc.identifier | http://arxiv.org/abs/math/0210424 | |
| dc.identifier | Topology and its Applications 140 (2004), 227-243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155717 | |
| dc.subject | General Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 54C55, 54F45 | |
| dc.title | Extension dimension for paracompact spaces | |
| dc.type | text |