On two questions on selectively highly divergent spaces

Angelo Bella; Santi Spadaro

paper

On two questions on selectively highly divergent spaces

arXiv:2309.11954

Abstract

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

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