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Some properties of quasiuniform multifunction spaces

Part of: Maps and general types of spaces defined by maps Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

Jiling Cao ,
Ivan L. Reilly  and
Salvador Romaguera
Jiling Cao
Affiliation:
Department of Mathematics The University of AucklandPrivate Bag 92019 Auckland 1, New Zealand
Ivan L. Reilly
Affiliation:
Department of Mathematics The University of AucklandPrivate Bag 92019 Auckland 1, New Zealand
Salvador Romaguera
Affiliation:
Escuela de Caminos Departmento de Matemática Aplicada Universidad Politécnica de Valencia46071 Valencia, Spain
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Abstract

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The aim of this paper is to explore some properties of quasiuniform multifunction spaces. Various kinds of completeness of the quasiuniform multifunction space (YmX, UmX) are characterized in terms of suitable properties of the range space (Y, U). We also discuss the local compactness of quasiuniform multifunction spaces. By using the notion of small-set symmetry, the classic result of Hunsaker and Naimpally is extended to the quasiuniform setting.

Keywords

Quasiuniformmultifunctioncompletestable filterVietoris topology..

MSC classification

Secondary: 54C35: Function spaces 54C60: Set-valued maps 54E15: Uniform structures and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 2 , April 1998 , pp. 169 - 177
Copyright
Copyright © Australian Mathematical Society 1998

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