Decompositions of direct products of groups
We propose a new method for the decomposition of direct products of groups into U subsets. By using this method, we prove the following generalization of the Comfort-van Mill theorem: An arbitrary nondiscrete topological Abelian group with a finite number of second-order elements can be decomposed i...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5136 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511339052531712 |
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| author | Protasov, I. V. Протасов, І. В. |
| author_facet | Protasov, I. V. Протасов, І. В. |
| author_sort | Protasov, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:25:28Z |
| description | We propose a new method for the decomposition of direct products of groups into U subsets. By using this method, we prove the following generalization of the Comfort-van Mill theorem: An arbitrary nondiscrete topological Abelian group with a finite number of second-order elements can be decomposed into a countable number of dense subsets. |
| first_indexed | 2026-03-24T03:11:19Z |
| format | Article |
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| id | umjimathkievua-article-5136 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:11:19Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/26/66e3612c2290302fd76c4a7eedbd0526.pdf |
| spelling | umjimathkievua-article-51362020-03-18T21:25:28Z Decompositions of direct products of groups Разбиения прямых произведений групп Protasov, I. V. Протасов, І. В. We propose a new method for the decomposition of direct products of groups into U subsets. By using this method, we prove the following generalization of the Comfort-van Mill theorem: An arbitrary nondiscrete topological Abelian group with a finite number of second-order elements can be decomposed into a countable number of dense subsets. Запропоновано новий метод розбиття прямих добутків груп на U-щільні підмножини. Цим методом доведено узагальнення теореми Комфорта - ван Мілла, яке полягає в тому, що довільну недискретну топологічну абелеву группу зі скінченним числом елементів порядку 2 можна розбити на зліченне число щільних підмножин. Institute of Mathematics, NAS of Ukraine 1997-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5136 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 10 (1997); 1385–1395 Український математичний журнал; Том 49 № 10 (1997); 1385–1395 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5136/6968 https://umj.imath.kiev.ua/index.php/umj/article/view/5136/6969 Copyright (c) 1997 Protasov I. V. |
| spellingShingle | Protasov, I. V. Протасов, І. В. Decompositions of direct products of groups |
| title | Decompositions of direct products of groups |
| title_alt | Разбиения прямых произведений групп |
| title_full | Decompositions of direct products of groups |
| title_fullStr | Decompositions of direct products of groups |
| title_full_unstemmed | Decompositions of direct products of groups |
| title_short | Decompositions of direct products of groups |
| title_sort | decompositions of direct products of groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5136 |
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