<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we deal with the properties (<italic>a</italic>)<italic>R</italic>-star-semi-Lindelöf and (<italic>a</italic>)<italic>M</italic>-star-semi-Lindelöf in (<italic>a</italic>)topological spaces. These properties are interesting as every (<italic>a</italic>)<italic>Rs</italic>-separable space is (<italic>a</italic>)<italic>R</italic>-star-semi-Lindelöf and every (<italic>a</italic>)<italic>s</italic>-semi-Lindelöf space is (<italic>a</italic>)<italic>R</italic>-star-semi-Lindelöf but not every (<italic>a</italic>)<italic>R</italic>-star-semi-Lindelöf space is (<italic>a</italic>)<italic>Rs</italic>-separable or (<italic>a</italic>)<italic>s</italic>-semi-Lindelöf. It is shown that if an (<italic>a</italic>)topological space <italic>X</italic> is the union of countably many (<italic>a</italic>)-open and (<italic>a</italic>)<italic>R</italic>star-semi-Lindelöf subspaces, then <italic>X</italic> is (<italic>a</italic>)<italic>R</italic>-star-semi-Lindelöf. Similar results are obtained in the context of (<italic>a</italic>)<italic>M</italic>-star-semi-Lindelöf spaces. Further, suitable and required counterexamples are given.
</abstract>

In this paper, we deal with the properties (a)R-star-semi-Lindelöf and (a)M-star-semi-Lindelöf in (a)topological spaces. These properties are interesting as every (a)Rs-separable space is (a)R-star-semi-Lindelöf and every (a)s-semi-Lindelöf space is (a)R-star-semi-Lindelöf but not every (a)R-star-semi-Lindelöf space is (a)Rs-separable or (a)s-semi-Lindelöf. It is shown that if an (a)topological space X is the union of countably many (a)-open and (a)Rstar-semi-Lindelöf subspaces, then X is (a)R-star-semi-Lindelöf. Similar results are obtained in the context of (a)M-star-semi-Lindelöf spaces. Further, suitable and required counterexamples are given.

Selective Version of Star-Semi-Lindelöfness in (<italic>a</italic>) Topological Spaces

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Selective Version of Star-Semi-Lindelöfness in () Topological Spaces

In this paper, we deal with the properties (a)R-star-semi-Lindelöf and (a)M-star-semi-Lindelöf in (a)topological spaces. These properties are interesting as...

Selective Version of Star-Semi-Lindelöfness in (a) Topological Spaces

Published Online: Nov 29, 2022

Page range: 39 - 56

Received: Apr 30, 2021

DOI: https://doi.org/10.2478/tmmp-2022-0002

Keywords
selection principles, selective separability, star covering, semi-Lindelöf, ()topological spaces

© 2022 Sheetal Luthra et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Selective Version of Star-Semi-Lindelöfness in (a) Topological Spaces

Published Online: Nov 29, 2022

Page range: 39 - 56

Received: Apr 30, 2021

DOI: https://doi.org/10.2478/tmmp-2022-0002

Keywordsselection principles, selective separability, star covering, semi-Lindelöf, ()topological spaces

© 2022 Sheetal Luthra et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
selection principles, selective separability, star covering, semi-Lindelöf, ()topological spaces