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Homogeneity of powers of spaces and the character
Author(s):
A.
V.
Arhangel'skii
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2165-2172.
MSC (2000):
Primary 54A25, 54B10
Posted:
February 18, 2005
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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:
10.1090/S0002-9939-05-07774-9
PII:
S 0002-9939(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
Posted:
February 18, 2005
Communicated by:
Alan Dow
Copyright of article:
Copyright
2005,
American Mathematical Society
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