Normality in the space of subgroups of the Lie group
It is proved that a connected Lie group is solvable if and only if the space of closed subgroups of this group is normal in the Vietoris topology and any compact segment of subgroups lying in this space is countable.
Saved in:
| Date: | 1990 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1990
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8837 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513322229563392 |
|---|---|
| author | Panasyuk, S. P. Панасюк, С. П. |
| author_facet | Panasyuk, S. P. Панасюк, С. П. |
| author_sort | Panasyuk, S. P. |
| 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 a connected Lie group is solvable if and only if the space of closed subgroups of this group is normal in the Vietoris topology and any compact segment of subgroups lying in this space is countable. |
| first_indexed | 2026-03-24T03:42:50Z |
| format | Article |
| fulltext |
0064-2
Page 1
0065
Page 1
0066-k
Page 1
|
| id | umjimathkievua-article-8837 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:42:50Z |
| publishDate | 1990 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b6/3a580d2a01fe9d917153956d77b34fb6.pdf |
| spelling | umjimathkievua-article-88372024-11-14T10:10:56Z Normality in the space of subgroups of the Lie group Нормальность в пространстве подгрупп группы Ли Panasyuk, S. P. Панасюк, С. П. It is proved that a connected Lie group is solvable if and only if the space of closed subgroups of this group is normal in the Vietoris topology and any compact segment of subgroups lying in this space is countable. Доказано, что связная группа Ли разрешима тогда и только тогда, когда пространство замкнутых подгрупп этой группы в топологии Вьеториса нормально и всякий компактный отрезок подгрупп, лежащий в этом пространстве, счетен. Доведено, що зв’язна група Лі, яку можна розв’язати тоді і тільки тоді, коли простір замкнутих підгруп цієї групи в топології В’єторіса нормальний і всякий компактний відрізок, який лежить у цьому просторі, зліченний. Institute of Mathematics, NAS of Ukraine 1990-06-19 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8837 Ukrains’kyi Matematychnyi Zhurnal; Vol. 42 No. 6 (1990); 786-788 Український математичний журнал; Том 42 № 6 (1990); 786-788 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8837/10258 Copyright (c) 1990 S. P. Panasyuk |
| spellingShingle | Panasyuk, S. P. Панасюк, С. П. Normality in the space of subgroups of the Lie group |
| title | Normality in the space of subgroups of the Lie group |
| title_alt | Нормальность в пространстве подгрупп группы Ли |
| title_full | Normality in the space of subgroups of the Lie group |
| title_fullStr | Normality in the space of subgroups of the Lie group |
| title_full_unstemmed | Normality in the space of subgroups of the Lie group |
| title_short | Normality in the space of subgroups of the Lie group |
| title_sort | normality in the space of subgroups of the lie group |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8837 |
| work_keys_str_mv | AT panasyuksp normalityinthespaceofsubgroupsoftheliegroup AT panasûksp normalityinthespaceofsubgroupsoftheliegroup AT panasyuksp normalʹnostʹvprostranstvepodgruppgruppyli AT panasûksp normalʹnostʹvprostranstvepodgruppgruppyli |