An example of a non-Borel locally-connected finite-dimensional topological group
Journal Title: Карпатські математичні публікації - Year 2017, Vol 9, Issue 1
Abstract
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 natural number $n$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of dimension $n$, 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.
Authors and Affiliations
I. Banakh, T. Banakh, M. Vovk
Keywords
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- EP ID EP324716
- DOI 10.15330/cmp.9.1.3-5
- Views 63
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