6533b822fe1ef96bd127d773

RESEARCH PRODUCT

P-spaces and the Volterra property

Santi Spadaro

subject

Pure mathematicsProperty (philosophy)Volterra spaceprimary 54E52 54G10 secondary 28A05General MathematicsHausdorff spaceGeneral Topology (math.GN)Mathematics::General TopologyBaire spaceBaire spacedensity topology.Volterra spaceNonlinear Sciences::Exactly Solvable and Integrable SystemsIntersectionProduct (mathematics)P-spaceFOS: MathematicsQuantitative Biology::Populations and EvolutionSubspace topologyMathematicsMathematics - General Topology

description

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.

yearjournalcountryeditionlanguage
2012-12-22
10.1017/s0004972712000585http://hdl.handle.net/20.500.11769/244521