On some questions on selectively highly divergent spaces

Abstract

A topological space X is selectively highly divergent (SHD) if for every sequence of non-empty open sets { Un : n ∈ ω } of X, we can find xn ∈ Un such that the sequence {xn : n ∈ ω } has no convergent subsequences. In this note we answer two questions related to this notion asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta.

Keywords

• convergent sequences
• splitting number
• stone-cech compactification
• selectively highly divergent spaces
• pixley-roy hyper-space