TO A QUESTION ON THE SUPERCOMPACTNESS OF ULTRAFILTER SPACES
The space of ultrafilters of a \(\pi\)-system endowed with the topology of Wallman type is considered. The question on the supercompactness of this space is investigated. For this, the enveloping space of maximal linked systems with the corresponding topology of Wallman type is used. Necessary and s...
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| Format: | Article |
| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2019-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/146 |
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| Summary: | The space of ultrafilters of a \(\pi\)-system endowed with the topology of Wallman type is considered. The question on the supercompactness of this space is investigated. For this, the enveloping space of maximal linked systems with the corresponding topology of Wallman type is used. Necessary and sufficient conditions for the coincidence of the set of all ultrafilters of the initial \(\pi\)-system and the set of all maximal linked systems for this \(\pi\)-system are obtained. Specific variants of wide sense measurable spaces with this coincidence property are given. |
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| ISSN: | 2414-3952 |