On Regularly Branched Maps
| dc.creator | Tuncali, H. Murat | |
| dc.creator | Valov, Vesko | |
| dc.date | 2003-01-24 | |
| dc.date | 2004-09-20 | |
| dc.date.accessioned | 2026-07-07T04:54:41Z | |
| dc.date.available | 2026-07-07T04:54:41Z | |
| dc.description | Let $f\colon X\to Y$ be a perfect map between finite-dimensional metrizable spaces and $p\geq 1$. It is shown that the space $C^*(X,\R^p)$ of all bounded maps from $X$ into $\R^p$ with the source limitation topology contains a dense $G_δ$-subset consisting of $f$-regularly branched maps. Here, a map $g\colon X\to\R^p$ is $f$-regularly branched if, for every $n\geq 1$, the dimension of the set $\{z\in Y\times\R^p: |(f\times g)^{-1}(z)|\geq n\}$ is $\leq n\cdot\big(\dim f+\dim Y\big)-(n-1)\cdot\big(p+\dim Y\big)$. This is a parametric version of the Hurewicz theorem on regularly branched maps. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301293 | |
| dc.identifier | http://arxiv.org/abs/math/0301293 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66352 | |
| dc.subject | General Topology | |
| dc.subject | 54F45; 55M10; 54C65 | |
| dc.title | On Regularly Branched Maps | |
| dc.type | text |