Irresolvable topologies on groups
We prove that there exist ZFC models in which every nondiscrete topological Abelian group can be decomposed into countably many dense subsets. This statement is an answer to the question raised by Comfort and van Mill. We also prove that every submaximal left-topological Abelian group is σ-discrete....
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| Date: | 1998 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4784 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510961495965696 |
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| author | Protasov, I. V. Протасов, И. В. Протасов, И. В. |
| author_facet | Protasov, I. V. Протасов, И. В. Протасов, И. В. |
| author_sort | Protasov, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:14:27Z |
| description | We prove that there exist ZFC models in which every nondiscrete topological Abelian group can be decomposed into countably many dense subsets. This statement is an answer to the question raised by Comfort and van Mill. We also prove that every submaximal left-topological Abelian group is σ-discrete. |
| first_indexed | 2026-03-24T03:05:19Z |
| format | Article |
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| id | umjimathkievua-article-4784 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:05:19Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/4e/f45047b9d61eec813c492cc01b2bc64e.pdf |
| spelling | umjimathkievua-article-47842020-03-18T21:14:27Z Irresolvable topologies on groups Неразложимые топологии на группах Protasov, I. V. Протасов, И. В. Протасов, И. В. We prove that there exist ZFC models in which every nondiscrete topological Abelian group can be decomposed into countably many dense subsets. This statement is an answer to the question raised by Comfort and van Mill. We also prove that every submaximal left-topological Abelian group is σ-discrete. Доведено існування моделей ZFC, в яких кожну недискретну топологічну абелеву групу можна розкласти на зліченне число щільних підмножин. Це твердження є відповіддю на запитання, поставлене Комфортом та ван Міллом. Показано, що кожна субмаксимальна лівотопологічиа абелева група σ-дискретна. Institute of Mathematics, NAS of Ukraine 1998-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4784 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 12 (1998); 1646–1655 Український математичний журнал; Том 50 № 12 (1998); 1646–1655 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4784/6268 https://umj.imath.kiev.ua/index.php/umj/article/view/4784/6269 Copyright (c) 1998 Protasov I. V. |
| spellingShingle | Protasov, I. V. Протасов, И. В. Протасов, И. В. Irresolvable topologies on groups |
| title | Irresolvable topologies on groups |
| title_alt | Неразложимые топологии на группах |
| title_full | Irresolvable topologies on groups |
| title_fullStr | Irresolvable topologies on groups |
| title_full_unstemmed | Irresolvable topologies on groups |
| title_short | Irresolvable topologies on groups |
| title_sort | irresolvable topologies on groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4784 |
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