On all kinds of homogeneous spaces

Ungar, Gerald S.

doi:10.1090/S0002-9947-1975-0385825-3

On all kinds of homogeneous spaces
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by Gerald S. Ungar PDF

Trans. Amer. Math. Soc. 212 (1975), 393-400 Request permission

Abstract:

Several open questions on homogeneous spaces are answered. A few of the results are: (1) An n-homogeneous metric continuum, which is not the circle, is strongly n-homogeneous. (2) A 2-homogeneous metric continuum is locally connected. (3) If X is a homogeneous compact metric space or a homogeneous locally compact, locally connected separable metric space, then X is a coset space. (4) If G is a complete separable metric topological group with is n-connected, then G is locally n-connected.

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