An example of a non-Borel locally-connected finite-dimensional topological group
According to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of dimension $\dim(G)=n$, which is not locally compact....
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Vasyl Stefanyk Precarpathian National University
2017-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1440 |
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doaj-d5c2106df3f44251bb4ccca1f89b36122020-11-25T03:15:13ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102017-06-01913510.15330/cmp.9.1.3-51440An example of a non-Borel locally-connected finite-dimensional topological groupI.Ya. Banakh0T.O. Banakh1M.I. Vovk2Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, UkraineIvan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, UkraineLviv Polytechnic National University, 12 Bandera str., 79013, Lviv, UkraineAccording to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of dimension $\dim(G)=n$, which is not locally compact. This answers a question posed by S. Maillot on MathOverflow and shows that the local path-connectedness in the result of Gleason and Montgomery can not be weakened to the local connectedness.https://journals.pnu.edu.ua/index.php/cmp/article/view/1440topological grouplie group |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
I.Ya. Banakh T.O. Banakh M.I. Vovk |
| spellingShingle |
I.Ya. Banakh T.O. Banakh M.I. Vovk An example of a non-Borel locally-connected finite-dimensional topological group Karpatsʹkì Matematičnì Publìkacìï topological group lie group |
| author_facet |
I.Ya. Banakh T.O. Banakh M.I. Vovk |
| author_sort |
I.Ya. Banakh |
| title |
An example of a non-Borel locally-connected finite-dimensional topological group |
| title_short |
An example of a non-Borel locally-connected finite-dimensional topological group |
| title_full |
An example of a non-Borel locally-connected finite-dimensional topological group |
| title_fullStr |
An example of a non-Borel locally-connected finite-dimensional topological group |
| title_full_unstemmed |
An example of a non-Borel locally-connected finite-dimensional topological group |
| title_sort |
example of a non-borel locally-connected finite-dimensional topological group |
| publisher |
Vasyl Stefanyk Precarpathian National University |
| series |
Karpatsʹkì Matematičnì Publìkacìï |
| issn |
2075-9827 2313-0210 |
| publishDate |
2017-06-01 |
| description |
According to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of dimension $\dim(G)=n$, which is not locally compact. This answers a question posed by S. Maillot on MathOverflow and shows that the local path-connectedness in the result of Gleason and Montgomery can not be weakened to the local connectedness. |
| topic |
topological group lie group |
| url |
https://journals.pnu.edu.ua/index.php/cmp/article/view/1440 |
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