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A non-homogeneous zero-dimensional is a group

Authors:	Fons van Engelen

Institution:	Erasmus Universiteit, Econometrisch Instituut, Postbus 1738, 3000~DR~~Rotterdam, The Netherlands

Abstract:	We provide an example of a zero-dimensional (separable metric) absolute Borel set 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 such that is a homogeneous non-group but $Y \times Y$ is a group. This answers questions of Arhangel'skii and Zhou.

Keywords:	Zero-dimensional Borel Wadge hierarchy homogeneous

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