Selections and order-like relations

Valentin Gutev

South Africa

University of Natal

School of Mathematical and Statistical Sciences

Faculty of Science

Tsugunori Nogura

Japan

Ehime University

Department of Mathematics

Faculty of Science

Submitted: 2014-02-17

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Accepted: 2014-02-17

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Published: 2001-10-01

DOI: https://doi.org/10.4995/agt.2001.2150
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Keywords:

Hyperspaces topology, Selection, Monotone selection, Ordered space

Supporting agencies:

This research was not funded

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.

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