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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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