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

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- by Fons van Engelen
- Proc. Amer. Math. Soc.
**124**(1996), 2589-2598 - DOI: https://doi.org/10.1090/S0002-9939-96-03561-7
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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’skiĭ and Zhou.## References

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## Bibliographic Information

**Fons van Engelen**- Affiliation: Erasmus Universiteit, Econometrisch Instituut, Postbus 1738, 3000 DR Rotterdam, The Netherlands
- Email: engelen@wis.few.eur.nl
- Received by editor(s): February 20, 1995
- Communicated by: Franklin D. Tall
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**124**(1996), 2589-2598 - MSC (1991): Primary 54H05, 54E35, 54F65; Secondary 03E15
- DOI: https://doi.org/10.1090/S0002-9939-96-03561-7
- MathSciNet review: 1346990