Selections and order-like relations

Valentin Gutev, Tsugunori Nogura

Abstract

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.


Keywords

Hyperspaces topology; Selection; Monotone selection; Ordered space

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1. Weak selections and weak orderability of function spaces
Valentin Gutev
Czechoslovak Mathematical Journal  vol: 60  issue: 1  first page: 273  year: 2010  
doi: 10.1007/s10587-010-0015-5



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e-ISSN: 1989-4147   https://doi.org/10.4995/agt