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July, 2012 On uniquely homogeneous spaces, I
Alexander ARHANGEL′SKII, Jan VAN MILL
J. Math. Soc. Japan 64(3): 903-926 (July, 2012). DOI: 10.2969/jmsj/06430903

Abstract

It is shown that all uniquely homogeneous spaces are connected. We characterize the uniquely homogeneous spaces that are semitopological or quasitopological groups. We identify two properties of homogeneous spaces called skew-2-flexibility and 2-flexibility that are useful in studying unique homogeneity. We also construct a large family of uniquely homogeneous spaces with only trivial continuous maps.

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Alexander ARHANGEL′SKII. Jan VAN MILL. "On uniquely homogeneous spaces, I." J. Math. Soc. Japan 64 (3) 903 - 926, July, 2012. https://doi.org/10.2969/jmsj/06430903

Information

Published: July, 2012
First available in Project Euclid: 24 July 2012

MathSciNet: MR2965432
Digital Object Identifier: 10.2969/jmsj/06430903

Subjects:
Primary: 54C05
Secondary: 54G20 , 54H05 , 54H11 , 54H15

Keywords: homogeneity , linearly ordered space , Polish space , product , quasitopological group , semitopological group , Topological Group , unique homogeneity

Rights: Copyright © 2012 Mathematical Society of Japan

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Vol.64 • No. 3 • July, 2012
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