Year: 2012
Type: preprint
Abstract: We show, in particular, that a multivalued map $f$ from a closed subspace $X$ of $\mathbb R^n$ to ${\rm exp}_k(\mathbb R^n)$ has a point of period exactly $M$ if and only if its continuous extension $\tilde f: βX\to {\rm exp}_k(β\mathbb R^n)$ has such a point. The result also holds if one repace $\mathbb R^n$ by a locally compact Lindelöf space of finite dimension. We also show that if $f$ is a colorable map froma normal space $X$ to the space ${\mathcal K}(X)$ of all compact subsets of $X$ then its extension $\tilde f:βX\to {\mathcal K}(βX)$ is fixed-point free.
Source: arXiv (Cornell University)
Authors: Buzyakova, R. Z., Chigogidze, A.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2617891778