Resumen de Selections generating new topologies

Valentin Gutev, Artur Hideyuki Tomita

• 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].