6533b851fe1ef96bd12a9783

RESEARCH PRODUCT

Countably compact weakly Whyburn spaces

Santi Spadaro

subject

Discrete mathematicsSingletonGeneralizationGeneral Mathematics010102 general mathematicsGeneral Topology (math.GN)Mathematics::General TopologyPrivate communicationUrysohn and completely Hausdorff spacesWeak Whyburn property convergence Lindelof P -space Urysohn countably compact pseudoradial.Space (mathematics)01 natural sciences010101 applied mathematicsCombinatoricsMathematics::LogicCardinalityFOS: MathematicsRegular spaceSettore MAT/03 - GeometriaContinuum (set theory)0101 mathematicsMathematicsMathematics - General Topology

description

The weak Whyburn property is a generalization of the classical sequential property that was studied by many authors. A space X is weakly Whyburn if for every non-closed set \({A \subset X}\) there is a subset \({B \subset A}\) such that \({\overline{B} \setminus A}\) is a singleton. We prove that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and show that, consistently, the Urysohn assumption is essential. We also give conditions for a (countably compact) weakly Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Angelo Bella in private communication.

yearjournalcountryeditionlanguage
2015-05-22
http://arxiv.org/abs/1505.06238