Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-16T01:16:37.102Z Has data issue: false hasContentIssue false
  • English
  • Français

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 [email protected]
TSUGUNORI NOGURA
Affiliation:
Department of Mathematics, Faculty of Science, Ehime University, Matsuyama, 790 [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)