Mesocompactness and selection theory

Peng-fei Yan; Zhongqiang Yang

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 1, page 149-157
  • ISSN: 0010-2628

Abstract

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A topological space X is called mesocompact (sequentially mesocompact) if for every open cover 𝒰 of X , there exists an open refinement 𝒱 of 𝒰 such that { V 𝒱 : V K } 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.

How to cite

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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 -

References

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  1. Boone J.R., Some characterization of paracompactness in χ -space, Fund. Math. 72 (1971), 145–155. MR0295291
  2. Choban M., Many-valued mappings and Borel sets, II, Trans. Moscow Math. Soc. 23 (1970), 286–310. 
  3. Engelking R., General Topology, Revised and completed edition, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  4. Michael E., 10.1215/S0012-7094-59-02662-6, Duke Math. 26 (1956), 647–652. MR0109343DOI10.1215/S0012-7094-59-02662-6
  5. Michael E., 10.1090/S0002-9947-1951-0042109-4, Trans. Amer. Math. Soc. 71 (1951), 152–182. Zbl0043.37902MR0042109DOI10.1090/S0002-9947-1951-0042109-4
  6. Miyazaki K., 10.1090/S0002-9939-01-06204-9, Proc. Amer. Math. Soc. 129 (2001), 2777–2782. Zbl0973.54009MR1838802DOI10.1090/S0002-9939-01-06204-9
  7. Nedev S., Selection and factorization theorems for set-valued mapings, Serdica 6 (1980), 291–317. MR0644284
  8. Yan P.-F., τ selections and its applictions on BCO, J. Math. (in Chinese) 17 (1997), 547–551. MR1675535

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