Geodesic
Weak orderability of some spaces which admit a weak selection
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 609-615

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We show that if a Hausdorff topological space $X$ satisfies one of the following properties: \noindent a) $X$ has a countable, discrete dense subset and $X^2$ is hereditarily collectionwise Hausdorff; \noindent b) $X$ has a discrete dense subset and admits a countable base; \noindent 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.
Classification : 54C65, 54D15, 54D70, 54E35, 54F05
Keywords: weak (continuous) selection; weak orderability; Vietoris topology; dense countable subset; isolated point; countable base; collectionwise Hausdorff space 
@article{CMUC_2006__47_4_a5,
     author = {Costantini, Camillo},
     title = {Weak orderability of some spaces which admit a weak selection},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {609--615},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2006},
     mrnumber = {2337415},
     zbl = {1150.54020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a5/}
}
TY  - JOUR
AU  - Costantini, Camillo
TI  - Weak orderability of some spaces which admit a weak selection
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 609
EP  - 615
VL  - 47
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a5/
LA  - en
ID  - CMUC_2006__47_4_a5
ER  - 
%0 Journal Article
%A Costantini, Camillo
%T Weak orderability of some spaces which admit a weak selection
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 609-615
%V 47
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a5/
%G en
%F CMUC_2006__47_4_a5
Costantini, Camillo. Weak orderability of some spaces which admit a weak selection. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 609-615. http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a5/