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.
Lingua originale | English |
---|---|
pagine (da-a) | 254-262 |
Numero di pagine | 9 |
Rivista | Acta Mathematica Hungarica |
Volume | 149 |
Stato di pubblicazione | Published - 2016 |
All Science Journal Classification (ASJC) codes
- ???subjectarea.asjc.2600.2600???