2015/05/22 by Santi Spadaro, Spadaro, Santi
Mathematics · #FOS: Mathematics #General Topology (math.GN) #math.GN
paper · pdf · doi:10.48550/arxiv.1505.06238
arxiv created 2015/11/18 · arxiv updated 2015/11/19
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.