Selections generating new topologies.

Gutev, Valentin, and Tomita, Artur. "Selections generating new topologies.." Publicacions Matemàtiques 51.1 (2007): 3-15. <http://eudml.org/doc/41884>.

@article{Gutev2007,
abstract = {Every (continuous) selection for the non-empty 2-point subsets of a space X naturally defines an interval-like topology on X. In the present paper, we demonstrate that, for a second-countable zero-dimensional space X, this topology may fail to be first-countable at some (or, even any) point of X. This settles some problems stated in [7].},
author = {Gutev, Valentin, Tomita, Artur},
journal = {Publicacions Matemàtiques},
keywords = {Espacios topológicos; Hiperespacio; Selecciones continuas; Hyperspace topology; Vietoris topology; continuous selection; weak selection},
language = {eng},
number = {1},
pages = {3-15},
title = {Selections generating new topologies.},
url = {http://eudml.org/doc/41884},
volume = {51},
year = {2007},
}

TY - JOUR
AU - Gutev, Valentin
AU - Tomita, Artur
TI - Selections generating new topologies.
JO - Publicacions Matemàtiques
PY - 2007
VL - 51
IS - 1
SP - 3
EP - 15
AB - Every (continuous) selection for the non-empty 2-point subsets of a space X naturally defines an interval-like topology on X. In the present paper, we demonstrate that, for a second-countable zero-dimensional space X, this topology may fail to be first-countable at some (or, even any) point of X. This settles some problems stated in [7].
LA - eng
KW - Espacios topológicos; Hiperespacio; Selecciones continuas; Hyperspace topology; Vietoris topology; continuous selection; weak selection
UR - http://eudml.org/doc/41884
ER -