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Homogeneity of powers of spaces and the character


Author: A. V. Arhangel'skii
Journal: Proc. Amer. Math. Soc. 133 (2005), 2165-2172
MSC (2000): Primary 54A25, 54B10
DOI: https://doi.org/10.1090/S0002-9939-05-07774-9
Published electronically: February 18, 2005
MathSciNet review: 2137884
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Abstract: A space is said to be power-homogeneous if some power of it is homogeneous. We prove that if a Hausdorff space $X$ of point-countable type is power-homogeneous, then, for every infinite cardinal $\tau $, the set of points at which $X$ has a base of cardinality not greater than $\tau $, is closed in $X$. Every power-homogeneous linearly ordered topological space also has this property. Further, if a linearly ordered space $X$ of point-countable type is power-homogeneous, then $X$ is first countable.


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Additional Information

A. V. Arhangel'skii
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: arhangel@math.ohiou.edu

DOI: https://doi.org/10.1090/S0002-9939-05-07774-9
Keywords: Power-homogeneous, point-countable type, $\tau$-twister, $\tau$-diagonalizable space, linearly ordered space, $G_\tau $-tightness, first countable space
Received by editor(s): August 25, 2003
Received by editor(s) in revised form: April 2, 2004
Published electronically: February 18, 2005
Communicated by: Alan Dow
Article copyright: © Copyright 2005 American Mathematical Society

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