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Star versions of Hurewicz spaces

Year 2021, Volume: 50 Issue: 5, 1325 - 1333, 15.10.2021

Sumit Singh Ljubiša D. R. Kočinac

https://doi.org/10.15672/hujms.819719
Cited By: 6

Abstract

A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of $X$ and each sequence $(\mathcal{U}_n: n\in \mathbb{N})$ of collections of sets open in $X$ such that for each $n\in \mathbb N$, $\overline{A} \subset \cup \mathcal{U}_n$, there is a sequence $(\mathcal{V}_n: n \in \mathbb{N})$ such that for each $n \in \mathbb{N}$, $\mathcal{V}_n$ is a finite subset of $\mathcal{U}_n$ and for each $x \in A$, $x \in {\rm St}(\cup\mathcal{V}_n, \mathcal{U}_n)$ for all but finitely many $n$. In this paper, we investigate the relationships among set star Hurewicz, set strongly star Hurewicz and other related covering properties and study the topological properties of these topological spaces.

Keywords

Hurewicz star-Hurewicz strongly star-Hurewicz set star Hurewicz set-SSH

References

  • [1] A.V. Arhangel’kii, A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carol. 36, 303–325, 1995.
  • [2] M. Bonanzinga and M.V. Matveev, Some covering properties for ψ-spaces, Mat. Vesnik 61, 3–11, 2009.
  • [3] M. Bonanzinga, F. Cammaroto and Lj.D.R. Kočinac, Star-Hurewicz and related properties, Appl. Gen. Topol. 5, 79–89, 2004.
  • [4] G. Di Maio and Lj.D.R. Kočinac, A note on quasi-Menger and similar spaces, Topology Appl. 179, 148–155, 2015.
  • [5] E.K. van Douwen, G.K. Reed, A.W. Roscoe and I.J. Tree, Star covering properties, Topology Appl. 39, 71–103, 1991.
  • [6] R. Engelking, General Topology, PWN, Warszawa, 1977.
  • [7] W. Hurewicz, Über die Verallgemeinerung des Borelshen Theorems, Math. Z. 24, 401–425, 1925.
  • [8] W. Hurewicz, Über Folgen stetiger Functionen, Fund. Math. 9, 193–204, 1927.
  • [9] Lj.D.R. Kočinac, Star-Menger and related spaces, Publ. Math. Debrecen 55, 421–431, 1999.
  • [10] Lj.D.R. Kočinac, Star-Menger and related spaces II, Filomat 13, 129–140, 1999.
  • [11] Lj.D.R. Kočinac, Addendum to: “Variations of classical selection principles: an overview", Quaest. Math., 2020. DOI: 10.2989/16073606.2020.1779501
  • [12] Lj,D.R. Kočinac and Ş. Konca, Set-Menger and related properties, Topology Appl. 275, Article No. 106996, 2020.
  • [13] Lj.D.R. Kočinac, Ş. Konca and S. Singh, Set star-Menger and set strongly star-Menger spaces, Math. Slovaca, in press.
  • [14] M.V. Matveev, A survey on star covering properties, Topology Atlas, Preprint No. 330, 1998.
  • [15] S. Mrówka, On completely regular spaces, Fund. Math. 41, 105–106, 1954.
  • [16] S. Singh, Remarks on set-Menger and related properties, Topology Appl. 280, Art. No. 107278, 2020.
  • [17] Y.K. Song, Remarks on strongly star-Hurewicz spaces, Filomat 27, 1127–1131, 2013.
  • [18] Y.K. Song, Remarks on star-Hurewicz spaces, Bull. Polish Acad. Sci. Math. 61, 247– 255, 2013.
  • [19] Y.K. Song, On star-K-Hurewicz spaces, Filomat 31, 1129–1285, 2017.
  • [20] Y.K. Song and Y.Y. Zhang, Some remarks on almost Lindelöf spaces and weakly Lindelöf spaces, Mat. Vesnik 62, 77–83, 2010.
  • [21] L.A. Steen and J.A. Seebach, Counterexamples in Topology, Dover Publications Inc., 1996.

Year 2021, Volume: 50 Issue: 5, 1325 - 1333, 15.10.2021

Sumit Singh Ljubiša D. R. Kočinac

https://doi.org/10.15672/hujms.819719
Cited By: 6

Abstract

References

  • [1] A.V. Arhangel’kii, A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carol. 36, 303–325, 1995.
  • [2] M. Bonanzinga and M.V. Matveev, Some covering properties for ψ-spaces, Mat. Vesnik 61, 3–11, 2009.
  • [3] M. Bonanzinga, F. Cammaroto and Lj.D.R. Kočinac, Star-Hurewicz and related properties, Appl. Gen. Topol. 5, 79–89, 2004.
  • [4] G. Di Maio and Lj.D.R. Kočinac, A note on quasi-Menger and similar spaces, Topology Appl. 179, 148–155, 2015.
  • [5] E.K. van Douwen, G.K. Reed, A.W. Roscoe and I.J. Tree, Star covering properties, Topology Appl. 39, 71–103, 1991.
  • [6] R. Engelking, General Topology, PWN, Warszawa, 1977.
  • [7] W. Hurewicz, Über die Verallgemeinerung des Borelshen Theorems, Math. Z. 24, 401–425, 1925.
  • [8] W. Hurewicz, Über Folgen stetiger Functionen, Fund. Math. 9, 193–204, 1927.
  • [9] Lj.D.R. Kočinac, Star-Menger and related spaces, Publ. Math. Debrecen 55, 421–431, 1999.
  • [10] Lj.D.R. Kočinac, Star-Menger and related spaces II, Filomat 13, 129–140, 1999.
  • [11] Lj.D.R. Kočinac, Addendum to: “Variations of classical selection principles: an overview", Quaest. Math., 2020. DOI: 10.2989/16073606.2020.1779501
  • [12] Lj,D.R. Kočinac and Ş. Konca, Set-Menger and related properties, Topology Appl. 275, Article No. 106996, 2020.
  • [13] Lj.D.R. Kočinac, Ş. Konca and S. Singh, Set star-Menger and set strongly star-Menger spaces, Math. Slovaca, in press.
  • [14] M.V. Matveev, A survey on star covering properties, Topology Atlas, Preprint No. 330, 1998.
  • [15] S. Mrówka, On completely regular spaces, Fund. Math. 41, 105–106, 1954.
  • [16] S. Singh, Remarks on set-Menger and related properties, Topology Appl. 280, Art. No. 107278, 2020.
  • [17] Y.K. Song, Remarks on strongly star-Hurewicz spaces, Filomat 27, 1127–1131, 2013.
  • [18] Y.K. Song, Remarks on star-Hurewicz spaces, Bull. Polish Acad. Sci. Math. 61, 247– 255, 2013.
  • [19] Y.K. Song, On star-K-Hurewicz spaces, Filomat 31, 1129–1285, 2017.
  • [20] Y.K. Song and Y.Y. Zhang, Some remarks on almost Lindelöf spaces and weakly Lindelöf spaces, Mat. Vesnik 62, 77–83, 2010.
  • [21] L.A. Steen and J.A. Seebach, Counterexamples in Topology, Dover Publications Inc., 1996.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sumit Singh 0000-0001-9701-3091

Ljubiša D. R. Kočinac 0000-0002-4870-7908

Publication Date October 15, 2021
Published in Issue Year 2021 Volume: 50 Issue: 5

Cite

APA Singh, S., & Kočinac, L. D. R. (2021). Star versions of Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics, 50(5), 1325-1333. https://doi.org/10.15672/hujms.819719
AMA Singh S, Kočinac LDR. Star versions of Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics. October 2021;50(5):1325-1333. doi:10.15672/hujms.819719
Chicago Singh, Sumit, and Ljubiša D. R. Kočinac. “Star Versions of Hurewicz Spaces”. Hacettepe Journal of Mathematics and Statistics 50, no. 5 (October 2021): 1325-33. https://doi.org/10.15672/hujms.819719.
EndNote Singh S, Kočinac LDR (October 1, 2021) Star versions of Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics 50 5 1325–1333.
IEEE S. Singh and L. D. R. Kočinac, “Star versions of Hurewicz spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 5, pp. 1325–1333, 2021, doi: 10.15672/hujms.819719.
ISNAD Singh, Sumit - Kočinac, Ljubiša D. R. “Star Versions of Hurewicz Spaces”. Hacettepe Journal of Mathematics and Statistics 50/5 (October 2021), 1325-1333. https://doi.org/10.15672/hujms.819719.
JAMA Singh S, Kočinac LDR. Star versions of Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics. 2021;50:1325–1333.
MLA Singh, Sumit and Ljubiša D. R. Kočinac. “Star Versions of Hurewicz Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 5, 2021, pp. 1325-33, doi:10.15672/hujms.819719.
Vancouver Singh S, Kočinac LDR. Star versions of Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics. 2021;50(5):1325-33.

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Some properties defined by relative versions of star-covering properties II
Applied General Topology
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On set star-Menger spaces
Quaestiones Mathematicae
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On some set properties
Filomat
https://doi.org/10.2298/FIL2219473M
On set star-Lindelöf spaces
Applied General Topology
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A note on set-star-K-Menger spaces
Mathematica Slovaca
https://doi.org/10.1515/ms-2022-0110

https://dergipark.org.tr/en/pub/hujms