6533b85efe1ef96bd12bfcbf
RESEARCH PRODUCT
P-spaces and the Whyburn property
A. BellaC. CostantiniSanti Spadarosubject
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 familydescription
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 weakly Whyburn, and we give a consistent example of a non-Whyburn product of two Lindel\"of Whyburn $P$-spaces.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-11-01 |