The weak Whyburn property is a generalization of the classical sequential property that has been studied by many authors. A space X is weakly Whyburn if for every non-closed set A⊂X there is a subset B⊂A such that B⎯⎯⎯⎯∖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) weak Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Bella in private communication.

SPADARO, S.D. (2016). Countably compact weakly Whyburn spaces. ACTA MATHEMATICA HUNGARICA, 149, 254-262 [10.1007/s10474-016-0611-4].

Countably compact weakly Whyburn spaces

SPADARO, SANTI DOMENICO
2016

Abstract

The weak Whyburn property is a generalization of the classical sequential property that has been studied by many authors. A space X is weakly Whyburn if for every non-closed set A⊂X there is a subset B⊂A such that B⎯⎯⎯⎯∖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) weak Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Bella in private communication.
Settore MAT/03 - Geometria
SPADARO, S.D. (2016). Countably compact weakly Whyburn spaces. ACTA MATHEMATICA HUNGARICA, 149, 254-262 [10.1007/s10474-016-0611-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/480962
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