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)

 

Homeomorphism groups of some direct limit spaces


Author: Margie Hale
Journal: Proc. Amer. Math. Soc. 85 (1982), 661-665
MSC: Primary 57S05; Secondary 54H15, 57N20, 58B05
MathSciNet review: 660625
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ F$ be either of the spaces $ {R^\infty } = {R^n}$ or $ {Q^\infty } = {Q^n}$ where $ R$ denotes the reals and $ Q$ the Hilbert cube. Let $ \mathcal{H}(M)$ be the homeomorphism group of a connected $ F$-manifold $ M$ with the compact-open topology. We prove that $ \mathcal{H}(M)$ is separable, Lindelöf, paracompact, non-first-countable, and not a $ k$-space.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57S05, 54H15, 57N20, 58B05

Retrieve articles in all journals with MSC: 57S05, 54H15, 57N20, 58B05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660625-4
PII: S 0002-9939(1982)0660625-4
Keywords: Homeomorphism group, direct limit, compact-open topology, manifold
Article copyright: © Copyright 1982 American Mathematical Society