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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the homeomorphism group of the rational numbers
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by Wayne R. Park PDF
Proc. Amer. Math. Soc. 42 (1974), 625-626 Request permission

Abstract:

Let Q be the rational numbers with the usual topology, $H(Q)$ the group of homeomorphisms of Q, ${\gamma _c}$ the convergence structure of continuous convergence, and $\sigma$ the coarsest admissible convergence structure which makes $H(Q)$ a convergence group. A counterexample is constructed to show that if $\kappa$ is a convergence structure on $H(Q)$ such that ${\gamma _c} \leqq \kappa \leqq \sigma$, then $\kappa$ is never principal, hence never topological.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 625-626
  • MSC: Primary 54A20; Secondary 57E05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0341368-9
  • MathSciNet review: 0341368