P-spaces and the Volterra property

Authors

  • Santi Spadaro York University

Keywords:

Baire, Volterra, $P$-space, almost $P$-space, weak $P$-space, density topology

Abstract

We study the relationship between generalizations of $P$-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two dense $G_\delta$ have dense (non-empty) 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 non-weakly 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 non-weakly Volterra subspace and is both a weak $P$-space and an almost $P$-space. 10.1017/S0004972712000585

Published

2013-02-24

Issue

Vol. 87 No. 2 (2013)

Section

Articles
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