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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on the homeomorphism group of the rational numbers

Author: Wayne R. Park
Journal: Proc. Amer. Math. Soc. 42 (1974), 625-626
MSC: Primary 54A20; Secondary 57E05
MathSciNet review: 0341368
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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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PII: S 0002-9939(1974)0341368-9
Article copyright: © Copyright 1974 American Mathematical Society