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 of point-countable type is power-homogeneous, then, for every infinite cardinal , the set of points at which has a base of cardinality not greater than , is closed in . Every power-homogeneous linearly ordered topological space also has this property. Further, if a linearly ordered space of point-countable type is power-homogeneous, then 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