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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

$\beta$-Menger and $\beta$-Hurewicz spaces

Memet Kule(KILIS 7 ARALIK UNIVERSITY)0000-0002-2869-2358
Pages
—
Publication Date
2022-02-14
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The subject of our investigation is also the preservation of $\beta $-Menger and $\beta $-Hurewicz properties under subspaces, products, and mappings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Recently, some papers on weaker forms of classical covering properties of Hurewicz and Menger have been published.
📊
Key Findings & Data:In this paper, using the covers formed by $\beta $-open sets, we introduce and study the properties of $\beta $-Menger and $\beta $-Hurewicz topological spaces.
💡
Conclusion & Impact:The subject of our investigation is also the preservation of $\beta $-Menger and $\beta $-Hurewicz properties under subspaces, products, and mappings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:β-open set · β-Menger space · β-Hurewicz space

Abstract

Recently, some papers on weaker forms of classical covering properties of Hurewicz and Menger have been published. In this paper, using the covers formed by $\beta $-open sets, we introduce and study the properties of $\beta $-Menger and $\beta $-Hurewicz topological spaces. We give counterexamples that show the interrelations between those properties. The subject of our investigation is also the preservation of $\beta $-Menger and $\beta $-Hurewicz properties under subspaces, products, and mappings.

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Cite This Article

Kule, M. (2022). $\beta$-Menger and $\beta$-Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.911145

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References (25)

  1. M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, $\beta $ -open sets and $\beta $-continuous mappings, Bull. Fac. Sci., Assiut Univ. 12, 77-90, 1983.
  2. M.E. Abd El-Monsef and A.M. Kozae, Some generalized forms of compactness and closedness, Delta J. Sci. 9 (2), 257-269, 1985.
  3. D. Andrijević, Semi-preopen sets, Mat. Vesnik, 38, 24-32, 1986.
  4. Aqsa and M.U.D. Khan, On nearly Menger and nearly star Menger spaces, Filomat, 33, 6219-6227, 2019.
  5. M. Caldas and S. Jafari, A new decomposition of $\beta $ -open functions, Chaos Solitons Fractals 40, 10-12, 2009.
  6. D. Chodounsky, D. Repovs and L. Zdomskyy, Mathias forcing and combinatorial covering properties of filters, J. Symb. Log. 80, 1398-1410, 2015.
  7. M. Ganster and D. Andrijević, On some questions concerning semi-preopen sets, J. Inst. Math. & Comp. Sci. (Math. Ser.) 1 (2), 65-75, 1988.
  8. W. Hurewicz, Über die Verallgemeinerung des Borelschen Theorems, Math. Z. 24, 401-425, 1925.
  9. W. Hurewicz, Über Folgen stetiger Functionen, Fund. Math. 9, 193-204, 1927.
  10. L.D.R. Kocinac, The Pixley-Roy topology and selection principles, Questions Answers Gen. Topology. 19, 219-225, 2001.
  11. L.D.R. Kocinac, Selected results on selection principles. Proceedings of the 3rd Semi- nar on Geometry & Topology, 71-104, Azarb. Univ. Tarbiat Moallem, Tabriz, 2004.
  12. L.D.R. Kocinac, Generalized open sets and selection properties, Filomat, 33, 1485- 1493, 2019.
  13. L.D.R. Kocinac, Variations of classical selection principles: An overview, Quaest. Math., 43 (8), 1121-1153, 2020.
  14. L.D.R. Kocinac, A. Sabah, M.U.D. Khan and D. Seba, Semi-Hurewicz spaces, Hacet. J. Math. Stat. 46 (1), 53-66, 2017.
  15. L.D.R. Kocinac and M. Scheepers, Combinatorics of open covers (VII): Groupability, Fund. Math. 179 (2), 131-155, 2003.
  16. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70, 36-41, 1963.
  17. A.S. Mashour, M.E. Abd El-Monsef and S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47-53, 1982.
  18. K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik (Wiener Akademie, Wien) 133, 421-444, 1924.
  19. A. Sabah, M.U.D. Khan and L.D.R. Ko˘cinac, Covering properties defined by semi- open sets, J. Nonlinear Sci. Appl. 9 (6), 4388-4398, 2016.
  20. M. Sakai, The weak Hurewicz property of Pixley-Roy hyperspaces, Topology Appl. 160, 2531-2537, 2013.
  21. M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topology Appl. 69, 31-62, 1996.
  22. M. Scheepers, Selection principles and covering properties in topology, Note Mat. 22 (2), 3-41, 2003.
  23. L.A. Steen and J.A. Seebach, Counterexamples in Topology, Holt, Rinehart and Win- ston, Inc., New York, 1970.
  24. B. Tsaban, Selection principles and special sets of reals, Open Problems in Topology II (E. Pearl, editor), Elsevier Science Publishing, Amsterdam, 91–108, 2007.
  25. B.K. Tyagi, S. Singh and M. Bhardwaj, Covering properties defined by preopen sets, Asian-European Journal of Mathematics, 14 (3), 2150035, 2021.