On two questions on selectively highly divergent spaces

Abstract

A topological space $X$ is selectively highly divergent (SHD) if for every sequence of non-empty open subsets $\{U_n: n\in \omega \}$ of $X$, we can pick a point $x_n\in U_n$, for every $n<\omega$, such that the sequence $\{x_n: n\in\omega\} $ has no convergent subsequences. In this note we answer four questions related to this notion asked in ArXiv:2307.11992.