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

In this article, we use the notion of ideals to study open covers and related selection principles, and thus, we extend some results in (Caserta et al. 2012; Chandra et al. 2020) where open covers and related selection principles have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notions of ℐ-<italic>γ</italic>ℬ <italic>s</italic> -cover, ℐ-strong-ℬ-Hurewicz and ℐ-strong-ℬ-groupable cover. Also, in (<italic>C</italic>(<italic>X</italic>),<italic>τ</italic>sℬ), some properties like ℐ-strictly Frèchet Urysohn, ℐ-Reznichenko property are investigated.
</abstract>

In this article, we use the notion of ideals to study open covers and related selection principles, and thus, we extend some results in (Caserta et al. 2012; Chandra et al. 2020) where open covers and related selection principles have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notions of ℐ-γℬ s -cover, ℐ-strong-ℬ-Hurewicz and ℐ-strong-ℬ-groupable cover. Also, in (C(X),τsℬ), some properties like ℐ-strictly Frèchet Urysohn, ℐ-Reznichenko property are investigated.

Some Observations on Ideal Variations of Bornological Covers

Tatra Mountains Mathematical Publications

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

{"article-title":"Some Observations on Ideal Variations of Bornological Covers"}

In this article, we use the notion of ideals to study open covers and related selection principles, and thus, we extend some results in (Caserta et al. 2012;...

Some Observations on Ideal Variations of Bornological Covers

Published Online: Nov 16, 2023

Page range: 1 - 16

Received: Jun 20, 2021

DOI: https://doi.org/10.2478/tmmp-2023-0020

Keywords
Bornology, selection principles, topology of strong uniform convergence, ℐ-convergence, open ℬ-cover, -cover, ℐ- -cover, ℐ- ℬ-Hurewicz property, ℐ-Reznichenko property, ℐ-strictly Frèchet Urysohn property

© 2023 Subhankar Das, published by Sciendo

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

Some Observations on Ideal Variations of Bornological Covers

Published Online: Nov 16, 2023

Page range: 1 - 16

Received: Jun 20, 2021

DOI: https://doi.org/10.2478/tmmp-2023-0020

KeywordsBornology, selection principles, topology of strong uniform convergence, ℐ-convergence, open ℬ-cover, -cover, ℐ- -cover, ℐ- ℬ-Hurewicz property, ℐ-Reznichenko property, ℐ-strictly Frèchet Urysohn property

© 2023 Subhankar Das, published by Sciendo

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

Keywords
Bornology, selection principles, topology of strong uniform convergence, ℐ-convergence, open ℬ-cover, -cover, ℐ- -cover, ℐ- ℬ-Hurewicz property, ℐ-Reznichenko property, ℐ-strictly Frèchet Urysohn property