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Volterra spaces revisited

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

Published online by Cambridge University Press:  09 April 2009

Jiling Cao  and
David Gauld
Jiling Cao
Affiliation:
Department of MathematicsThe University of AucklandPrivate Bag 92019Auckland 1New Zealand e-mail: jil.cao@auckland.ac.nz, d.gauld@auckland.ac.nz
David Gauld
Affiliation:
Department of MathematicsThe University of AucklandPrivate Bag 92019Auckland 1New Zealand e-mail: jil.cao@auckland.ac.nz, d.gauld@auckland.ac.nz
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Abstract

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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.

Keywords

Baire spacedense Gε-setthe Vietoris topologyVolterra spaceweakly Volterra space.

MSC classification

Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) 54C05: Continuous maps 54E52: Baire category, Baire spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 61 - 76
Copyright
Copyright © Australian Mathematical Society 2005

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