Vol. 60, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
B-complete and Br-complete topological algebras

Domenico Rosa

Vol. 60 (1975), No. 2, 199–208

In this note, a topological algebra A is an algebra over the field of complex numbers together with a Hausdorff locally convex topology which makes multiplication jointly continuous. A is called B-complete (Br-complete) if every continuous (continuous, one-to-one) and almost open algebra homomorphism from A onto any topological algebra is open. For a completely regular space X, C(X) is the algebra of all continuous complex-valued functions with the usual pointwise operations and the compact-open topology. The main theorem states that C(X) is a B-complete algebra iff X is a k-space.

Mathematical Subject Classification 2000
Primary: 46H20
Secondary: 46A30
Received: 6 February 1975
Published: 1 October 1975
Domenico Rosa