Selections and order-like relations

Abstract

<p>Every selection f for the family F<sub>2</sub>(X) of at most two-point subsets of a set X naturally defines an order-like relation on X by if and only . In the present paper we study the relationship between and the possible topologies T on X which realize the continuity of f with respect to the Vietoris topology on F<sub>2</sub>(X) generated by T.</p>