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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On all kinds of homogeneous spaces


Author: Gerald S. Ungar
Journal: Trans. Amer. Math. Soc. 212 (1975), 393-400
MSC: Primary 54H99; Secondary 54H15
MathSciNet review: 0385825
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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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DOI: https://doi.org/10.1090/S0002-9947-1975-0385825-3
Article copyright: © Copyright 1975 American Mathematical Society