Arnautov's problems on semitopological isomorphisms
Semitopological isomorphisms of topological groups were introduced by Arnautov [2], who posed several questions related to compositions of semitopological isomorphisms and about the groups G (we call them Arnautov groups) such that for every group topology on G every semitopological isomorphism wit...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2009-04-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1789 |
| _version_ | 1818163390161354752 |
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| author | Dikran Dikranjan Anna Giordano Bruno |
| author_facet | Dikran Dikranjan Anna Giordano Bruno |
| author_sort | Dikran Dikranjan |
| collection | DOAJ |
| description | Semitopological isomorphisms of topological groups were introduced by Arnautov [2], who posed several questions related to compositions of semitopological isomorphisms and about the groups G (we call them Arnautov groups) such that for every group topology on G every semitopological isomorphism with domain (G, ) is necessarily open (i.e., a topological isomorphism). We propose a different approach to these problems by introducing appropriate new notions, necessary for a deeper understanding of Arnautov groups. This allows us to find some partial answers and many examples. In particular, we discuss the relation with minimal groups and non-topologizable groups. |
| first_indexed | 2024-12-11T16:48:48Z |
| format | Article |
| id | doaj.art-72b2a35d70ca4ce596b0f77e0e676def |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-11T16:48:48Z |
| publishDate | 2009-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-72b2a35d70ca4ce596b0f77e0e676def2022-12-22T00:58:09ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472009-04-011018511910.4995/agt.2009.17891449Arnautov's problems on semitopological isomorphismsDikran Dikranjan0Anna Giordano Bruno1Università di UdineUniversità di UdineSemitopological isomorphisms of topological groups were introduced by Arnautov [2], who posed several questions related to compositions of semitopological isomorphisms and about the groups G (we call them Arnautov groups) such that for every group topology on G every semitopological isomorphism with domain (G, ) is necessarily open (i.e., a topological isomorphism). We propose a different approach to these problems by introducing appropriate new notions, necessary for a deeper understanding of Arnautov groups. This allows us to find some partial answers and many examples. In particular, we discuss the relation with minimal groups and non-topologizable groups.http://polipapers.upv.es/index.php/AGT/article/view/1789A-complete topologyHeisenberg groupMarkov groupMinimal groupOpen mapping theoremPermutations groupSemitopological isomorphismTaımanov topologyTopologizable group |
| spellingShingle | Dikran Dikranjan Anna Giordano Bruno Arnautov's problems on semitopological isomorphisms Applied General Topology A-complete topology Heisenberg group Markov group Minimal group Open mapping theorem Permutations group Semitopological isomorphism Taımanov topology Topologizable group |
| title | Arnautov's problems on semitopological isomorphisms |
| title_full | Arnautov's problems on semitopological isomorphisms |
| title_fullStr | Arnautov's problems on semitopological isomorphisms |
| title_full_unstemmed | Arnautov's problems on semitopological isomorphisms |
| title_short | Arnautov's problems on semitopological isomorphisms |
| title_sort | arnautov s problems on semitopological isomorphisms |
| topic | A-complete topology Heisenberg group Markov group Minimal group Open mapping theorem Permutations group Semitopological isomorphism Taımanov topology Topologizable group |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1789 |
| work_keys_str_mv | AT dikrandikranjan arnautovsproblemsonsemitopologicalisomorphisms AT annagiordanobruno arnautovsproblemsonsemitopologicalisomorphisms |