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.
Angelo Bella, Santi Spadaro (2024). On some questions on selectively highly divergent spaces. APPLIED GENERAL TOPOLOGY, 25(1), 41-46 [10.4995/agt.2024.20387].
On some questions on selectively highly divergent spaces
Angelo Bella;Santi Spadaro
2024-04-02
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.
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