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Research Article | Open Access

Compactness and axioms of countability in soft hyperspaces

G. Şenel1( ), J. I. Baek2( ), S. H. Han3, M. Cheong4( ), K. Hur3
Department of Mathematics, University of Amasya, 05100 Amasya, Turkey
School of Big Data and Financial Statistics, Wonkwang University, Korea
Division of Applied Mathematics, Wonkwang University, Korea
School of Liberal Arts and Sciences, Korea Aerospace University, Korea
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Abstract

In this paper, we studied the compactness relationships, the local compactness relationships, the separability, and the axiom of countability relationships in a soft topological space and its soft hyperspaces. In particular, the compactness relationships, the local compactness relationships, the separability, and the axiom of countability relationships in a classical topological space and its hyperspace were treated as corollaries.

Keywords

soft topological spacesoft Ti-space (i = 0, 1, 2, 3, 4)soft compactnesssoft local compactnesssoft separabilitysoft axioms of countabilitysoft hyperspace
CLC number: 54A40, 54B20, 54D10, 54D15

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 72-96
DOI: 10.3934/math.2025005

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Cite this article:
Şenel G, Baek JI, Han SH, et al. Compactness and axioms of countability in soft hyperspaces. AIMS Mathematics, 2025, 10(1): 72-96. https://doi.org/10.3934/math.2025005

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Received: 10 September 2024
Revised: 14 November 2024
Accepted: 05 December 2024
Published: 15 January 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)