Some remarks on selectively highly divergent spaces

Luong Quoc Tuyen

https://orcid.org/0000-0002-4330-0746

Viet Nam

University of Da Nang image/svg+xml

Department of Mathematics

Nguyen Xuan Truc

https://orcid.org/0009-0009-2696-5365

Viet Nam

University of Da Nang image/svg+xml

Department of Mathematics

Submitted: 2024-08-22

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Accepted: 2025-11-05

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Published: 2026-02-24

DOI: https://doi.org/10.4995/agt.22295

Copyright (c) 2025 Luong Quoc Tuyen, Nguyen Xuan Truc, Ong Van Tuyen

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Keywords:

convergent sequence, Selectively highly divergent spaces, Pixley-Roy hyperspace, Vietoris hyperspace, quasi-perfect mapping, quasi-open mapping

Supporting agencies:

This research was not funded

Abstract:

In this paper, we study selectively highly divergent (SHD) spaces on hyperspaces with the Vietoris topology and the Pixley-Roy topology. Moreover, we show that they are preserved under quasi-perfect countable-to-one mappings and preserved inversely under quasi-open mappings.

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References:

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