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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homogeneity in powers
of subspaces of the real line


Author: L. Brian Lawrence
Journal: Trans. Amer. Math. Soc. 350 (1998), 3055-3064
MSC (1991): Primary 54B10; Secondary 54E35, 54F99
MathSciNet review: 1458308
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Abstract | References | Similar Articles | Additional Information

Abstract: Working in ZFC, we prove that for every zero-dimensional subspace $S$ of the real line, the Tychonoff power ${}^\omega S$ is homogeneous ($\omega$ denotes the nonnegative integers). It then follows as a corollary that ${}^\omega S$ is homogeneous whenever $S$ is a separable zero-dimensional metrizable space. The question of homogeneity in powers of this type was first raised by Ben Fitzpatrick, and was subsequently popularized by Gary Gruenhage and Hao-xuan Zhou.


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Additional Information

L. Brian Lawrence
Affiliation: Department of Mathematics, George Mason University, Fairfax, Virginia 22030-4444
Email: blawrenc@osf1.gmu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02100-X
PII: S 0002-9947(98)02100-X
Keywords: Real line, separable metric space, zero-dimensional, subspace, product space, power, homogeneous, rigid
Received by editor(s): September 7, 1994
Received by editor(s) in revised form: June 1, 1995
Article copyright: © Copyright 1998 American Mathematical Society