• Corpus ID: 119604697

An example of a non-Borel locally-connected finite-dimensional topological group

@inproceedings{IBanakh2016AnEO,
  title={An example of a non-Borel locally-connected finite-dimensional topological group},
  author={I.Banakh and T.Banakh and M.Vovk},
  year={2016}
}
Answering a question posed by S.Maillot in MathOverFlow, for every n ∈ N we construct a locally connected subgroup G ⊂ Rn+1 of dimension dim(G) = n, which is not locally compact. By a classical result of Gleason [3] and Montgomery [6], every locally pathconnected finite-dimensional topological group G is locally compact. Generalizing this result of Gleason and Montgomery, Banakh and Zdomskyy [1] proved that a topological group G is locally compact if G is compactly finite-dimensional and… 

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mail address: t.o.banakh@gmail.com I.Banakh: Ya. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv E-mail address: ibanakh@yahoo