Some properties of quasiuniform
multifunction spaces

Jiling Cao
Department of Mathematics
The University of Auckland
Private Bag 92019
Auckland 1
New Zealand
and
Ivan L. Reilly
Department of Mathematics
The University of Auckland
Private Bag 92019
Auckland 1
New Zealand
and
Salvador Romaguera
Escuela de Caminos
Departamento de Matemática Aplicada
Universidad Politécnica de Valencia
46071 Valencia
Spain

Abstract:

The aim of this paper is to explore some properties of quasiuniform multifunction spaces. Various kinds of completeness of the quasiuniform multifunction space $(Y^{mX}, {\cal U}_{mX})$ are characterized in terms of suitable properties of the range space $(Y, {\cal U})$. 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.

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