When is a Volterra space Baire?

Cao, Jiling; Junnila, Heikki J. K.

doi:10.1016/j.topol.2006.05.009

Cited by 3 publications

(3 citation statements)

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“…From the above characterization it's clear that every Baire space is Volterra. The problem of when a Volterra space is Baire has been studied extensively (see [3] and [8]). This note was inspired by the simple observation that every P -space (that is, a space where every G δ set is open) is hereditarily Volterra.…”

Section: Proposition 12 [7]mentioning

confidence: 99%

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P-SPACES AND THE VOLTERRA PROPERTY

Spadaro

2012

Bull. Aust. Math. Soc.

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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 G δ 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.2010 Mathematics subject classification: primary 54E52, 54G10; secondary 28A05.

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Section: Proposition 12 [7]mentioning

confidence: 99%

“…From the above characterisation it is clear that every Baire space is Volterra. The problem of when a Volterra space is Baire has been extensively studied (see [2,7]).…”

Section: Introductionmentioning

confidence: 99%

P-SPACES AND THE VOLTERRA PROPERTY

Spadaro

2012

Bull. Aust. Math. Soc.

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“…The class of Volterra spaces was introduced in [9]. See [3], [4], [7], [8], [11] and for more information about Volterra spaces.…”

Section: (X) or Dg(x)mentioning

confidence: 99%

Almost Gp-Spaces

Mohammad¹

2010

Journal of the Korean Mathematical Society

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Abstract. A T 1 topological space X is called an almost GP-space if every dense G δ -set of X has nonempty interior. The behaviour of almost GP-spaces under taking subspaces and superspaces, images and preimages and products is studied. If each dense G δ -set of an almost GP-space X has dense interior in X, then X is called a GID-space. In this paper, some interesting properties of GID-spaces are investigated. We will generalize some theorems that hold in almost P-spaces.

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Edge of the World: When Are Manifolds Metrisable?

Gauld

2014

Non-Metrisable Manifolds

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When is a Volterra space Baire?

Cited by 3 publications

References 10 publications

P-SPACES AND THE VOLTERRA PROPERTY

P-SPACES AND THE VOLTERRA PROPERTY

Almost Gp-Spaces

Edge of the World: When Are Manifolds Metrisable?

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