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Closed Locally Path-connected Subspaces of Finite-dimensional Groups Are Locally Compact by Banakh, Taras; Zdomskyy, Lyubomyr is a scholarly article available to read on EtoBox.

What is Closed Locally Path-connected Subspaces of Finite-dimensional Groups Are Locally Compact about?

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 spaces that are not homeomorphic to closed subsets of finite-dimensional topological groups, which answers in negative a question of D.Shakhmatov. Another corollary is a characterization of Lie groups as finite-dimensional locally continuum-connected topological groups. For locally path connected topological groups this characterization was proved by Gleason and Palais in 1957.

Author

Banakh, Taras; Zdomskyy, Lyubomyr

Published

2015

Language

EN