Restorability of the Vietoris topology according to the compacts in the space of closed subgroups
It is proved that the space of closed subgroups ${\mathfrak L} (G)$ of a locally compact $\sigma$-compact group $G$ is a $k$-space if and only if each noncompact subgroup of $G$ can be represented as the intersection of a countable number of open sets.
Збережено в:
| Дата: | 1990 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1990
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8838 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513323940839424 |
|---|---|
| author | Piskunov, A. G. Пискунов, А. Г. |
| author_facet | Piskunov, A. G. Пискунов, А. Г. |
| author_sort | Piskunov, A. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-11-14T10:10:56Z |
| description | It is proved that the space of closed subgroups ${\mathfrak L} (G)$ of a locally compact $\sigma$-compact group $G$ is a $k$-space if and only if each noncompact subgroup of $G$ can be represented as the intersection of a countable number of open sets. |
| first_indexed | 2026-03-24T03:42:52Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8838 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:42:52Z |
| publishDate | 1990 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f5/20b48f98f7accca0b45d749d2f520cf5.pdf |
| spelling | umjimathkievua-article-88382024-11-14T10:10:56Z Restorability of the Vietoris topology according to the compacts in the space of closed subgroups Восстанавливаемость топологии Вьеториса по компактам в пространстве замкнутых подгрупп Piskunov, A. G. Пискунов, А. Г. It is proved that the space of closed subgroups ${\mathfrak L} (G)$ of a locally compact $\sigma$-compact group $G$ is a $k$-space if and only if each noncompact subgroup of $G$ can be represented as the intersection of a countable number of open sets. Доказано, что пространство замкнутых подгрупп ${\mathfrak L} (G)$ локально компактной $\sigma$-компактной группы $G$ является $k$-пространством тогда и только тогда, когда каждая некомпактная подгруппа из $G$ представима в виде пересечения счетного числа открытых множеств. Доведено, що простір замкнених підгруп ${\mathfrak L} (G)$ локально компактної $\sigma$-компактної групи $G$ є $k$-простором тоді і тільки тоді, коли кожна некомпактна підгрупа із $G$ може бути представлена у вигляді перетину зліченної кількості відкритих множин. Institute of Mathematics, NAS of Ukraine 1990-06-19 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8838 Ukrains’kyi Matematychnyi Zhurnal; Vol. 42 No. 6 (1990); 789-794 Український математичний журнал; Том 42 № 6 (1990); 789-794 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8838/10259 Copyright (c) 1990 A. G. Piskunov |
| spellingShingle | Piskunov, A. G. Пискунов, А. Г. Restorability of the Vietoris topology according to the compacts in the space of closed subgroups |
| title | Restorability of the Vietoris topology according to the compacts in the space of closed subgroups |
| title_alt | Восстанавливаемость топологии Вьеториса по компактам в пространстве замкнутых подгрупп |
| title_full | Restorability of the Vietoris topology according to the compacts in the space of closed subgroups |
| title_fullStr | Restorability of the Vietoris topology according to the compacts in the space of closed subgroups |
| title_full_unstemmed | Restorability of the Vietoris topology according to the compacts in the space of closed subgroups |
| title_short | Restorability of the Vietoris topology according to the compacts in the space of closed subgroups |
| title_sort | restorability of the vietoris topology according to the compacts in the space of closed subgroups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8838 |
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