Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A20, 57E05

Retrieve articles in all journals with MSC: 54A20, 57E05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0341368-9
PII: S 0002-9939(1974)0341368-9
Article copyright: © Copyright 1974 American Mathematical Society