Pettis property for Polish inverse semigroups
We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2023-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/17396 |
| _version_ | 1797668484011786240 |
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| author | Karen Arana Jerson Pérez Carlos Uzcátegui |
| author_facet | Karen Arana Jerson Pérez Carlos Uzcátegui |
| author_sort | Karen Arana |
| collection | DOAJ |
| description | We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity. |
| first_indexed | 2024-03-11T20:29:52Z |
| format | Article |
| id | doaj.art-08ce412493bd4018ae5570f7f6ef45cb |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-03-11T20:29:52Z |
| publishDate | 2023-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-08ce412493bd4018ae5570f7f6ef45cb2023-10-02T09:44:07ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472023-10-0124245546710.4995/agt.2023.1739616585Pettis property for Polish inverse semigroupsKaren Arana0https://orcid.org/0000-0002-2868-6695Jerson Pérez1Carlos Uzcátegui2https://orcid.org/0000-0002-3452-2312Industrial University of SantanderIndustrial University of SantanderIndustrial University of SantanderWe study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.https://polipapers.upv.es/index.php/AGT/article/view/17396inverse topological semigroupspolish semigroupspettis theoremautomatic continuity |
| spellingShingle | Karen Arana Jerson Pérez Carlos Uzcátegui Pettis property for Polish inverse semigroups Applied General Topology inverse topological semigroups polish semigroups pettis theorem automatic continuity |
| title | Pettis property for Polish inverse semigroups |
| title_full | Pettis property for Polish inverse semigroups |
| title_fullStr | Pettis property for Polish inverse semigroups |
| title_full_unstemmed | Pettis property for Polish inverse semigroups |
| title_short | Pettis property for Polish inverse semigroups |
| title_sort | pettis property for polish inverse semigroups |
| topic | inverse topological semigroups polish semigroups pettis theorem automatic continuity |
| url | https://polipapers.upv.es/index.php/AGT/article/view/17396 |
| work_keys_str_mv | AT karenarana pettispropertyforpolishinversesemigroups AT jersonperez pettispropertyforpolishinversesemigroups AT carlosuzcategui pettispropertyforpolishinversesemigroups |