You are currently offline. Some features of the site may not work correctly.

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… Expand

We prove that each closed locally continuum- connected subspace of a finite dimensional topological group is locally compact. This allows us to construct many 1-dimensional metrizable separable… Expand

Proceedings of the National Academy of Sciences of the United States of America

1950

TLDR

Together with Theorem 2 and the results for cyclic groups, these Theorems prove that any abelian homology or cohomology group A,(II) or Af(II, J) may be computed in a finite number of steps.Expand

The classical descriptive set theory is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.Expand

IN reviewing Dr. F. W. Lanchester's book “The Theory of Dimensions and its Application for Engineers” in NATURE of January 9, I stated with regard to Appendix VI that “in my opinion the author was… Expand

A non locally compact group of finite topological dimension

MathOverFlow

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