Öz
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.
Anahtar Kelimeler
Hurewicz star-Hurewicz strongly star-Hurewicz set star Hurewicz set-SSH
Kaynakça
- [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.
Öz
Kaynakça
- [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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Ekim 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 50 Sayı: 5 |