J. Aust. Math. Soc.  79 (2005), 61-76

Volterra spaces revisited

Jiling Cao   Department of Mathematics   The University of Auckland   Private Bag 92019   Auckland 1   New Zealand   jil.cao@auckland.ac.nz and David Gauld   Department of Mathematics   The University of Auckland   Private Bag 92019   Auckland 1   New Zealand   d.gauld@auckland.ac.nz

Abstract

In this paper, we investigate Volterra spaces and relevant topological properties. New characterizations of weakly Volterra spaces are provided. An analogy of the Banach category theorem in terms of Volterra properties is obtained. It is shown that every weakly Volterra homogeneous space is Volterra, and there are metrizable Baire spaces whose hyperspaces of nonempty compact subsets endowed with the Vietoris topology are not weakly Volterra.

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