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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: 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

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