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  • P-SPACES AND THE VOLTERRA PROPERTY

  • Part of
  • SANTI SPADARO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 2 / April 2013
    Published online by Cambridge University Press:
    31 July 2012, pp. 339-345
    Print publication:
    April 2013
    • Article
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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.