Weak orderability of some spaces which admit a weak selection
Commentationes Mathematicae Universitatis Carolinae (2006)
- Volume: 47, Issue: 4, page 609-615
- ISSN: 0010-2628
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topCostantini, Camillo. "Weak orderability of some spaces which admit a weak selection." Commentationes Mathematicae Universitatis Carolinae 47.4 (2006): 609-615. <http://eudml.org/doc/249840>.
@article{Costantini2006,
abstract = {We show that if a Hausdorff topological space $X$ satisfies one of the following properties:
a) $X$ has a countable, discrete dense subset and $X^2$ is hereditarily collectionwise Hausdorff;
b) $X$ has a discrete dense subset and admits a countable base;
then the existence of a (continuous) weak selection on $X$ implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.},
author = {Costantini, Camillo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weak (continuous) selection; weak orderability; Vietoris topology; dense countable subset; isolated point; countable base; collectionwise Hausdorff space; weak (continuous) selection; weak orderability; Vietoris topology; dense countable subset},
language = {eng},
number = {4},
pages = {609-615},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Weak orderability of some spaces which admit a weak selection},
url = {http://eudml.org/doc/249840},
volume = {47},
year = {2006},
}
TY - JOUR
AU - Costantini, Camillo
TI - Weak orderability of some spaces which admit a weak selection
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 4
SP - 609
EP - 615
AB - We show that if a Hausdorff topological space $X$ satisfies one of the following properties:
a) $X$ has a countable, discrete dense subset and $X^2$ is hereditarily collectionwise Hausdorff;
b) $X$ has a discrete dense subset and admits a countable base;
then the existence of a (continuous) weak selection on $X$ implies weak orderability. As a special case of either item a) or b), we obtain the result for every separable metrizable space with a discrete dense subset.
LA - eng
KW - weak (continuous) selection; weak orderability; Vietoris topology; dense countable subset; isolated point; countable base; collectionwise Hausdorff space; weak (continuous) selection; weak orderability; Vietoris topology; dense countable subset
UR - http://eudml.org/doc/249840
ER -
References
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