Weak selections and weak orderability of function spaces

Gutev, Valentin. "Weak selections and weak orderability of function spaces." Czechoslovak Mathematical Journal 60.1 (2010): 273-281. <http://eudml.org/doc/38006>.

@article{Gutev2010,
abstract = {It is proved that for a zero-dimensional space $X$, the function space $C_p(X,2)$ has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if $X$ is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space $E$, the function space $C_p(X,E)$ is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial positive answer to a question posed by van Mill and Wattel.},
author = {Gutev, Valentin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Vietoris hyperspace; continuous selection; function space; weakly orderable space; Vietoris hyperspace; continuous selection; function space; weakly orderable space},
language = {eng},
number = {1},
pages = {273-281},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak selections and weak orderability of function spaces},
url = {http://eudml.org/doc/38006},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Gutev, Valentin
TI - Weak selections and weak orderability of function spaces
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 273
EP - 281
AB - It is proved that for a zero-dimensional space $X$, the function space $C_p(X,2)$ has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if $X$ is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space $E$, the function space $C_p(X,E)$ is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial positive answer to a question posed by van Mill and Wattel.
LA - eng
KW - Vietoris hyperspace; continuous selection; function space; weakly orderable space; Vietoris hyperspace; continuous selection; function space; weakly orderable space
UR - http://eudml.org/doc/38006
ER -