Search results for "54G10"

showing 3 items of 3 documents

P-spaces and the Whyburn property

2009

We investigate the Whyburn and weakly Whyburn property in the class of $P$-spaces, that is spaces where every countable intersection of open sets is open. We construct examples of non-weakly Whyburn $P$-spaces of size continuum, thus giving a negative answer under CH to a question of Pelant, Tkachenko, Tkachuk and Wilson. In addition, we show that the weak Kurepa Hypothesis (a set-theoretic assumption weaker than CH) implies the existence of a non-weakly Whyburn $P$-space of size $\aleph_2$. Finally, we consider the behavior of the above-mentioned properties under products; we show in particular that the product of a Lindel\"of weakly Whyburn P-space and a Lindel\"of Whyburn $P$-space is we…

Mathematics::General TopologyFOS: Mathematicsnowhere MAD familyP-space; Whyburn space; weakly Whyburn space; Lindelöf space; pseudoradial space; radial space; radial character; ω-modification; cardinality; weight; extent; pseudocharacter; almost disjoint family; nowhere MAD family; Continuum Hypothesis; week Kurepa treepseudocharacterweakly Whyburn spaceMathematics - General Topologyradial spacealmost disjoint familyω-modificationweek Kurepa treeGeneral Topology (math.GN)weightContinuum HypothesisLindelof space54G10 54A20 54A35 54D20 54B10Whyburn spaceextentLindelöf spaceradial charactercardinalitypseudoradial spaceP-spaceSettore MAT/03 - Geometriaweak Kurepa tree.MAD family
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P-spaces and the Volterra property

2012

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…

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
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Noetherian type in topological products

2010

The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …

Topological manifoldFundamental groupTopological algebraGeneral MathematicsTopological tensor productGeneral Topology (math.GN)Noetherian typeMathematics::General TopologyMathematics - LogicTopological spaceChang’s conjectureTopologyTopological vector spaceTukey mapH-spaceMathematics::LogicFOS: MathematicsPCF theoryTopological ring03E04 54A25 (Primary) 03E55 54B10 54D70 54G10 (Secondary)Box productLogic (math.LO)Mathematics - General TopologyMathematics
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