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SELECTIONS FOR VIETORIS-LIKE HYPERSPACE TOPOLOGIES

Published online by Cambridge University Press:  01 January 2000

VALENTIN GUTEV  and
TSUGUNORI NOGURA
VALENTIN GUTEV
Affiliation:
School of Mathematics and Statistical Science, Faculty of Science, University of Natal, King George V Avenue, Durban 4041, South Africagutev@sci.und.ac.za
TSUGUNORI NOGURA
Affiliation:
Department of Mathematics, Faculty of Science, Ehime University, Matsuyama, 790 Japannogura@dpc.ehime-u.ac.jp
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Abstract

A general selection theorem for a Vietoris-like hyperspace topology is obtained and, as a result, several known selection theorems for both `topology'- and `metric'-generated hyperspace topologies are improved from a common point of view. Applications are presented in characterizing classes of metrizable spaces by continuous selections for their hyperspaces.

1991 Mathematics Subject Classification: primary 54B20, 54C65; secondary 54E45, 54D65, 54E40, 54C10, 54G12.

Keywords

hyperspace topologyselection$\tau$-continuous selection${\cal D}$-modified Vietoris topology${\cal D}$-orderable basestrongly zero-dimensional metrizable spacelocally compact metrizable space
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 80 , Issue 1 , January 2000 , pp. 235 - 256
Copyright
2000 London Mathematical Society

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