COUNTABLY COMPACT WEAKLY WHYBURN SPACES

Author(s)

Spadaro, S.

• Document type: Journal article
• Source: ACTA MATHEMATICA HUNGARICA; v. 149, n. 1, p. 254-262, JUN 2016.
• Web of Science Citations: 1

Abstract

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 of X there is a subset B subset of A such that (B) over bar \textbackslash{} 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. (AU)

• FAPESP's process: 13/14640-1 - Discrete sets and cardinal invariants in set-theoretic topology
• Grantee: Santi Domenico Spadaro
• Support Opportunities: Scholarships in Brazil - Post-Doctoral