P-SPACES AND THE VOLTERRA PROPERTY

Abstract

AbstractWe study the relationship between generalisations ofP-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two denseGδhave dense (nonempty) intersection. In particular, we prove that every dense and every open, but not every closed subspace of an almostP-space is Volterra and that there are Tychonoff nonweakly Volterra weakP-spaces. These results should be compared with the fact that everyP-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 weakP-space and an almostP-space.