On set star-Lindelöf spaces

Sumit Singh

doi:10.4995/agt.2022.17021

Authors

Sumit Singh University of Delhi https://orcid.org/0000-0001-9701-3091

DOI:

https://doi.org/10.4995/agt.2022.17021

Keywords:

Menger, Covering, Star-Covering, star-Lindelöf, strongly star-Lindelöf, set star-Lindelöf, topological space

Abstract

A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆⋃U, there is a countable subset V of U such that A ⊆ St (⋃V,U). The class of set star-Lindelöf spaces lie between the class of Lindel öf spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set star-Lindelöf spaces.

Downloads

Download data is not yet available.

Author Biography

Sumit Singh, University of Delhi

Department of Mathematics, Dyal Singh College

References

A. V. Arhangel'skii, An external disconnected bicompactum of weight c is inhomogeneous, Dokl. Akad. Nauk SSSR. 175 (1967), 751-754.

M. Bonanzinga and M. V. Matveev, Some covering properties for ψ-spaces, Mat. Vesnik. 61 (2009), 3-11.

M. Bonanzinga, Star Lindelöf and absolutely star-Lindelöf spaces, Quest. Answ. Gen. Topol. 16 (1998), 79-104.

M. Bonanzinga and F. Maesano, Some properties defined by relative versions of star-covering properties, Topology Appl. 306 (2022), Article no. 107923. https://doi.org/10.1016/j.topol.2021.107923

E. K. van Douwen, G. K. Reed, A. W. Roscoe and I. J. Tree, Star covering properties, Topology Appl. 39 (1991), 71-103. https://doi.org/10.1016/0166-8641(91)90077-Y

R. Engelking, General topology, PWN, Warszawa, 1977.

Lj. D. R. Kočinac and S. Konca, Set-Menger and related properties, Topology Appl. 275 (2020), Article no. 106996. https://doi.org/10.1016/j.topol.2019.106996

Lj. D. R. Kočinac, S. Konca and S. Singh, Set star-Menger and set strongly star-Menger spaces, Math. Slovaca 72 (2022), 185-196. https://doi.org/10.1515/ms-2022-0013

Lj. D. R. Kočinac and S. Singh, On the set version of selectively star-ccc spaces, J. Math. (2020) Article ID 9274503. https://doi.org/10.1155/2020/9274503

M. V. Matveev, A survey on star-covering properties, Topology Atlas, preprint No 330 1998.

S. Mrówka, On completely regular spaces, Fund. Math. 41 (1954), 105-106. https://doi.org/10.4064/fm-41-1-105-106

S. Singh, Set starcompact and related spaces, Afr. Mat. 32 (2021), 1389-1397. https://doi.org/10.1007/s13370-021-00906-5

S. Singh, Remarks on set-Menger and related properties, Topology Appl. 280 (2020), Article no. 107278. https://doi.org/10.1016/j.topol.2020.107278

S. Singh, On set-star-K-Hurewicz spaces, Bull. Belg. Math. Soc. Simon Stevin 28, no. 3 (2021), 361-372.

S. Singh, On set-star-K-Menger spaces, Publ. Math. Debrecen 100 (2022), 87-100. https://doi.org/10.5486/PMD.2022.9037

S. Singh, On set weak strongly star-Menger spaces, submitted.

S. Singh and Lj. D. R. Kočinac, Star versions of Hurewicz spaces, Hacet. J. Math. Stat. 50, no. 5 (2021), 1325-1333. https://doi.org/10.15672/hujms.819719

Y. K. Song, Remarks on neighborhood star-Lindelöf spaces, Filomat 27, no. 1 (2013), 149-155. https://doi.org/10.2298/FIL1301149S

Y. K. Song and W. F. Xuan, Remarks on new star-selection principles in topology, Topology Appl. 268 (2019), Paper no. 106921. https://doi.org/10.1016/j.topol.2019.106921

R. C. Walker, The stone-Čech compactification, Berlin, 1974. https://doi.org/10.1007/978-3-642-61935-9

W. F. Xuan and W. X. Shi, Notes on star Lindelöf spaces, Topology Appl. 204 (2016), 63-69. https://doi.org/10.1016/j.topol.2016.02.009