COUNTABLE COMPACTNESS MODULO AN IDEAL OF NATURAL NUMBERS
In this article, we introduce the idea of \(I\)-compactness as a covering property through ideals of \(\mathbb N\) and regardless of the \(I\)-convergent sequences of points. The frameworks of \(s\)-compactness, compactness and sequential compactness are compared to the structure of \(I\)-compact s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2023-12-01
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| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/626 |
| Summary: | In this article, we introduce the idea of \(I\)-compactness as a covering property through ideals of \(\mathbb N\) and regardless of the \(I\)-convergent sequences of points. The frameworks of \(s\)-compactness, compactness and sequential compactness are compared to the structure of \(I\)-compact space. We began our research by looking at some fundamental characteristics, such as the nature of a subspace of an \(I\)-compact space, then investigated its attributes in regular and separable space. Finally, various features resembling finite intersection property have been investigated, and a connection between \(I\)-compactness and sequential \(I\)-compactness has been established. |
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| ISSN: | 2414-3952 |