On some questions on selectively highly divergent spaces
Submitted: 2023-09-25
|Accepted: 2023-10-30
|Published: 2024-04-02
Copyright (c) 2023 Angelo Bella, Santi Spadaro
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Convergent sequences, Splitting number, Stone-Cech compactification, Selectively highly divergent spaces, Pixley-Roy hyper-space
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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.
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