Mathematics – General Topology
Scientific paper
2003-01-24
Mathematics
General Topology
12 pages
Scientific paper
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 $G_{\delta}$-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.
Tuncali Murat H.
Valov Vesko
No associations
LandOfFree
On Regularly Branched Maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Regularly Branched Maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Regularly Branched Maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-715421