On some questions on selectively highly divergent spaces

Angelo Bella; Santi Spadaro

doi:10.4995/agt.2024.20387

On some questions on selectively highly divergent spaces

Angelo Bella, Santi Spadaro

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 points x_n ∈ U_n, for every n < ω such that the sequence {x_n: n ∈ ω} has no convergent subsequences. In this note we answer four questions related to this notion that were asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta.

Original language	English
Pages (from-to)	41-46
Number of pages	6
Journal	Applied General Topology
Volume	25
Issue number	1
DOIs	https://doi.org/10.4995/agt.2024.20387
State	Published - 1 Jan 2024
Externally published	Yes

Keywords

convergent sequence
Pixley-Roy hyper-space
selectively highly divergent space
splitting number
Stone-Cech compacti-fication

ASJC Scopus subject areas

Geometry and Topology

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10.4995/agt.2024.20387

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N2 - 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 points xn ∈ Un, for every n < ω such that the sequence {xn: n ∈ ω} has no convergent subsequences. In this note we answer four questions related to this notion that were asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta.

AB - 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 points xn ∈ Un, for every n < ω such that the sequence {xn: n ∈ ω} has no convergent subsequences. In this note we answer four questions related to this notion that were asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta.

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On some questions on selectively highly divergent spaces

Abstract

Keywords

ASJC Scopus subject areas

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