Article
| Title: | Statistical convergence of order $\alpha$ in topology and its applications to selection principles (English) |
| Author: | Datta, Tanmayee |
| Author: | Bal, Prasenjit |
| Author: | Das, Parthiba |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 239-257 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The statistical convergence in a topological space is constrained in this study up to order $\alpha$, where $\alpha \in (0, 1)$. A fresh group of open covers (namely $s^{\alpha}$-$\gamma$ covers) and an entirely novel category of denseness (namely $s^{\alpha}$-denseness) are proposed using this notion of $s^{\alpha}$-convergence, which has been used to study various topological aspects of $s^{\alpha}$-density. It has been revealed that the class of $s^{\alpha}$-$\gamma$ coverings falls somewhere between the class of $\gamma$ covers and the class of $s$-$\gamma$ covers. The influence of $s^{\alpha}$-$\gamma$ covers in topological games and selection principles are also investigated. (English) |
| Keyword: | asymptotic density |
| Keyword: | statistical convergence |
| Keyword: | $\gamma$ cover |
| Keyword: | selection principle |
| MSC: | 54B20 |
| MSC: | 54C35 |
| MSC: | 54D20 |
| DOI: | 10.14712/1213-7243.2025.010 |
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| Date available: | 2025-11-12T15:49:03Z |
| Last updated: | 2025-11-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153171 |
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