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 { U_n : n ∈ ω } of X, we can find x_n ∈ Un such that the sequence {x_n : 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.