Discontinuous Birkhoff theorem
A topological space X is called totally recurrent if every mapping f : X → X has a recurrent point. We prove that a Hausdorff space X is totally recurrent if and only if X is either finite or a one-point compactification of an infinite discrete space.
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| Published in: | Український математичний вісник |
|---|---|
| Date: | 2007 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/124527 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Discontinuous Birkhoff theorem / O. Petrenko, I.V. Protasov // Український математичний вісник. — 2007. — Т. 4, № 3. — С. 434-436. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862736531367657472 |
|---|---|
| author | Petrenko, O. Protasov, I.V. |
| author_facet | Petrenko, O. Protasov, I.V. |
| citation_txt | Discontinuous Birkhoff theorem / O. Petrenko, I.V. Protasov // Український математичний вісник. — 2007. — Т. 4, № 3. — С. 434-436. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | A topological space X is called totally recurrent if every mapping f : X → X has a recurrent point. We prove that a Hausdorff space X is totally recurrent if and only if X is either finite or a one-point compactification of an infinite discrete space.
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| first_indexed | 2025-12-07T19:54:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124527 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T19:54:30Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Petrenko, O. Protasov, I.V. 2017-09-29T05:29:39Z 2017-09-29T05:29:39Z 2007 Discontinuous Birkhoff theorem / O. Petrenko, I.V. Protasov // Український математичний вісник. — 2007. — Т. 4, № 3. — С. 434-436. — Бібліогр.: 2 назв. — англ. 1810-3200 2000 MSC. 37B20, 54C10, 58K15. https://nasplib.isofts.kiev.ua/handle/123456789/124527 A topological space X is called totally recurrent if every mapping f : X → X has a recurrent point. We prove that a Hausdorff space X is totally recurrent if and only if X is either finite or a one-point compactification of an infinite discrete space. en Інститут прикладної математики і механіки НАН України Український математичний вісник Discontinuous Birkhoff theorem Article published earlier |
| spellingShingle | Discontinuous Birkhoff theorem Petrenko, O. Protasov, I.V. |
| title | Discontinuous Birkhoff theorem |
| title_full | Discontinuous Birkhoff theorem |
| title_fullStr | Discontinuous Birkhoff theorem |
| title_full_unstemmed | Discontinuous Birkhoff theorem |
| title_short | Discontinuous Birkhoff theorem |
| title_sort | discontinuous birkhoff theorem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124527 |
| work_keys_str_mv | AT petrenkoo discontinuousbirkhofftheorem AT protasoviv discontinuousbirkhofftheorem |