We study the relationship between generalizations of P-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two dense Gδ 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.

SPADARO, S.D. (2013). P-spaces and the Volterra property. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 87(2), 339-345 [10.1017/S0004972712000585].

P-spaces and the Volterra property

SPADARO, SANTI DOMENICO
2013

Abstract

We study the relationship between generalizations of P-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two dense Gδ 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.
https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/pspaces-and-the-volterra-property/ACE53B452EE72A931CBE0BC434B95124
SPADARO, S.D. (2013). P-spaces and the Volterra property. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 87(2), 339-345 [10.1017/S0004972712000585].
File in questo prodotto:
File Dimensione Formato  
Volterra.pdf

accesso aperto

Tipologia: Pre-print
Dimensione 120.63 kB
Formato Adobe PDF
120.63 kB Adobe PDF Visualizza/Apri
VolterraFinale.pdf

non disponibili

Tipologia: Versione Editoriale
Dimensione 133.19 kB
Formato Adobe PDF
133.19 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/480960
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact