Closure-preserving covers in function spaces
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 4, page 693-703
- ISSN: 0010-2628
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topSánchez, David Guerrero. "Closure-preserving covers in function spaces." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 693-703. <http://eudml.org/doc/246906>.
@article{Sánchez2010,
abstract = {It is shown that if $C_p(X)$ admits a closure-preserving cover by closed $\sigma $-compact sets then $X$ is finite. If $X$ is compact and $C_p(X)$ has a closure-preserving cover by separable subspaces then $X$ is metrizable. We also prove that if $C_p(X,[0,1])$ has a closure-preserving cover by compact sets, then $X$ is discrete.},
author = {Sánchez, David Guerrero},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {closure-preserving covers; function spaces; compact spaces; pointwise convergence topology; topological game; winning strategy; closure-preserving covers; function spaces; compact space; pointwise convergence topology; topological game; winning strategy},
language = {eng},
number = {4},
pages = {693-703},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Closure-preserving covers in function spaces},
url = {http://eudml.org/doc/246906},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Sánchez, David Guerrero
TI - Closure-preserving covers in function spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 4
SP - 693
EP - 703
AB - It is shown that if $C_p(X)$ admits a closure-preserving cover by closed $\sigma $-compact sets then $X$ is finite. If $X$ is compact and $C_p(X)$ has a closure-preserving cover by separable subspaces then $X$ is metrizable. We also prove that if $C_p(X,[0,1])$ has a closure-preserving cover by compact sets, then $X$ is discrete.
LA - eng
KW - closure-preserving covers; function spaces; compact spaces; pointwise convergence topology; topological game; winning strategy; closure-preserving covers; function spaces; compact space; pointwise convergence topology; topological game; winning strategy
UR - http://eudml.org/doc/246906
ER -
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