Journal of the Australian Mathematical Society - Series A Vol. 64 Part 2 (1998) 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. PDF file size: 64K © Copyright 1998, Australian Mathematical Society