The absolutely strongly star-Hurewicz property with respect to an ideal

Year, pages: 2020, 81 - 94

A space $X$ is said to have the absolutely strongly star-$ \mathcal{I} $-Hurewicz (ASS$ \mathcal{I} $H) property if for each sequence $ (\mathcal{U}_n: n \in \mathbb{N}) $ of open covers of $X$ and each dense subset $Y$ of $X$, there is a sequence $ (F_n: n \in \mathbb{N}) $ of finite subsets of $Y$ such that for each $ x \in X $, $ \{n \in \mathbb{N}: x \notin \St(F_n, \mathcal{U}_n) \} \in \mathcal{I}$, where $ \mathcal{I} $ is the proper admissible ideal of $ \mathbb{N} $. In this paper, we investigate the relationship between the ASS$ \mathcal{I} $H property and other related properties and study the topological properties of the ASS$\mathcal{I} $H property. This paper generalizes several results of Song [SYKH] to the larger class of spaces having the ASS$ \mathcal{I} $H properties.

Singh, S., Tyagi, B., Bhardwaj, V. 2020. The absolutely strongly star-Hurewicz property with respect to an ideal. In Tatra Mountains Mathematical Publications, vol. 76, no.2, pp. 81-94. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0020

Singh, S., Tyagi, B., Bhardwaj, V. (2020). The absolutely strongly star-Hurewicz property with respect to an ideal. Tatra Mountains Mathematical Publications, 76(2), 81-94. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0020

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

The Creative Commons Attribution-NC-ND 4.0 International Public License