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A non-homogeneous zero-dimensional $X$
such that $X \times X$ is a group

Author: Fons van Engelen
Journal: Proc. Amer. Math. Soc. 124 (1996), 2589-2598
MSC (1991): Primary 54H05, 54E35, 54F65; Secondary 03E15
MathSciNet review: 1346990
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Abstract: We provide an example of a zero-dimensional (separable metric) absolute Borel set $X$ which is not homogeneous, but whose square $X \times X$ admits the structure of a topological group. We also construct a zero-dimensional absolute Borel set $Y$ such that $Y$ is a homogeneous non-group but $Y \times Y$ is a group. This answers questions of Arhangel'skii and Zhou.

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Additional Information

Fons van Engelen
Affiliation: Erasmus Universiteit, Econometrisch Instituut, Postbus 1738, 3000 DR Rotterdam, The Netherlands

Keywords: Zero-dimensional, Borel, Wadge hierarchy, homogeneous
Received by editor(s): February 20, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society