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Date Published: 14/12/2024
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DOI: https://doi.org/10.52714/dthu.14.5.2025.1500
Issue
Vol. 14 No. 5 (2025): Natural Sciences Issue (English)
Section
Natural Sciences Issue (English)
How to Cite
Nguyen, X. T., Nguyen, T. H. P., Ong, V. T., & Luong, Q. T. (2024). ω-cover, k-cover and related spaces on the Pixley-Roy PR[X]. Dong Thap University Journal of Science, 14(5), 60-66. https://doi.org/10.52714/dthu.14.5.2025.1500

ω-cover, k-cover and related spaces on the Pixley-Roy PR[X]

Xuan Truc Nguyen1, , Thi Hong Phuc Nguyen1, Van Tuyen Ong2, Quoc Tuyen Luong1
1 Department of Mathematics, The University of Da Nang, Unversity of Science and Education, Vietnam
2 Hoa Vang High School, Da Nang City, Vietnam

Main Article Content

Abstract

In this paper, we study the concepts of ω-cover, k-cover and certain spaces defined by them on the hyperspace PR[X] of finite subsets of a space X endowed with the Pixley-Roy topology. We prove that PR[X] is an ω-Rothberger (resp., ω-Menger, ω-Lindelöf) space if and only if X is countable. Moreover, we show that PR[X] is a k-Lindelöf and first-countable space if and only if X is a countable and first-countable space.

Keywords

Pixley-Roy hyperspace, $omega$-cover, $k$-cover

Article Details

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References

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