A non-homogeneous zero-dimensional 𝑋 such that 𝑋×𝑋 is a group

van Engelen, Fons

doi:10.1090/S0002-9939-96-03561-7

A non-homogeneous zero-dimensional $X$ such that $X \times X$ is a group
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Proc. Amer. Math. Soc. 124 (1996), 2589-2598 Request permission

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’skiĭ and Zhou.

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