On set star-Lindelöf spaces
Submitted: 2022-01-16
|Accepted: 2022-04-18
|Published: 2022-10-03
Copyright (c) 2022 Applied General Topology
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Menger, Covering, Star-Covering, star-Lindelöf, strongly star-Lindelöf, set star-Lindelöf, topological space
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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.
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