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P-SPACES AND THE VOLTERRA PROPERTY

Part of: Spaces with richer structures Peculiar spaces

Published online by Cambridge University Press:  31 July 2012

SANTI SPADARO
SANTI SPADARO*
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, York University, Toronto, ON, Canada M3J 1P3 (email: santispadaro@yahoo.com)
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Abstract

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We study the relationship between generalisations of P-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two dense Gδ have dense (nonempty) intersection. In particular, we prove that every dense and every open, but not every closed subspace of an almost P-space is Volterra and that there are Tychonoff nonweakly Volterra weak P-spaces. These results should be compared with the fact that every P-space is hereditarily Volterra. As a byproduct we obtain an example of a hereditarily Volterra space and a hereditarily Baire space whose product is not weakly Volterra. We also show an example of a Hausdorff space which contains a nonweakly Volterra subspace and is both a weak P-space and an almost P-space.

Keywords

BaireVolterraP-spacealmost P-spaceweak P-spacedensity topology

MSC classification

Secondary: 54E52: Baire category, Baire spaces 54G10: $P$-spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 339 - 345
Copyright
©2012 Australian Mathematical Publishing Association Inc.

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