Selections and order-like relations

Valentin Gutev, Tsugunori Nogura


Every selection f for the family F2(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 F2(X) generated by T.


Hyperspaces topology; Selection; Monotone selection; Ordered space

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Universitat Politècnica de València

e-ISSN: 1989-4147