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].
@article{urn:eudml:doc:41884,
title = {Selections generating new topologies.},
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {3-15},
mrnumber = {MR2307144},
zbl = {1133.54005},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41884}
}
Gutev, Valentin; Tomita, Artur. Selections generating new topologies.. Publicacions Matemàtiques, (2007), pp. 3-15. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41884/