Vol. 44, No. 1, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Topological groups whose underlying spaces are separable Fréchet manifolds

James Edgar Keesling

Vol. 44 (1973), No. 1, 181–189
Abstract

Let G be a topological group and let G denote the space of all Lebesgue measurable functions from the unit interval [0,1] into G with the topology of convergence in measure. With this topology and with pointwise multiplication as the group operation, G is a topological group. If G is separable and has a complete metric and has more than one point, then Bessaga and Pefczyński have shown that G is homeomorphic to l2, separable infinite-dimensional Hilbert space. This fact is used in this paper to show the existence of separable Fréchet manifolds which are topological groups and which have certain algebraic and topological properties.

Mathematical Subject Classification 2000
Primary: 58B99
Secondary: 22A99
Milestones
Received: 10 August 1971
Revised: 20 March 1972
Published: 1 January 1973
Authors
James Edgar Keesling