Approximation by light maps and parametric Lelek maps

Details Approximation by light maps and parametric Lelek maps Approximation by light maps and parametric Lelek maps

2008-01-20

arxiv.org/abs/0801.3107v1

Mathematics

Geometric Topology

34 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Approximation by light maps and parametric Lelek 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 Approximation by light maps and parametric Lelek maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximation by light maps and parametric Lelek maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-593300