Mesocompactness and selection theory

Yan, Peng-fei, and Yang, Zhongqiang. "Mesocompactness and selection theory." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 149-157. <http://eudml.org/doc/246744>.

@article{Yan2012,
abstract = {A topological space $X$ is called mesocompact (sequentially mesocompact) if for every open cover $\{\mathcal \{U\}\}$ of $X$, there exists an open refinement $\{\mathcal \{V\}\}$ of $\{\mathcal \{U\}\}$ such that $\lbrace V\in \{\mathcal \{V\}\}: V\cap K\ne \emptyset \rbrace $ is finite for every compact set (converging sequence including its limit point) $K$ in $X$. In this paper, we give some characterizations of mesocompact (sequentially mesocompact) spaces using selection theory.},
author = {Yan, Peng-fei, Yang, Zhongqiang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {selections; l.s.c. set-valued maps; mesocompact; sequentially mesocompact; persevering compact set-valued maps; set-valued map; lower semi-continuous map; set-valued selection; compact-preserving map; sequentially mesocompact space},
language = {eng},
number = {1},
pages = {149-157},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Mesocompactness and selection theory},
url = {http://eudml.org/doc/246744},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Yan, Peng-fei
AU - Yang, Zhongqiang
TI - Mesocompactness and selection theory
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 149
EP - 157
AB - A topological space $X$ is called mesocompact (sequentially mesocompact) if for every open cover ${\mathcal {U}}$ of $X$, there exists an open refinement ${\mathcal {V}}$ of ${\mathcal {U}}$ such that $\lbrace V\in {\mathcal {V}}: V\cap K\ne \emptyset \rbrace $ is finite for every compact set (converging sequence including its limit point) $K$ in $X$. In this paper, we give some characterizations of mesocompact (sequentially mesocompact) spaces using selection theory.
LA - eng
KW - selections; l.s.c. set-valued maps; mesocompact; sequentially mesocompact; persevering compact set-valued maps; set-valued map; lower semi-continuous map; set-valued selection; compact-preserving map; sequentially mesocompact space
UR - http://eudml.org/doc/246744
ER -