Vol. 34, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 330: 1
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Locally compact spaces and two classes of Cāˆ—-algebras

Johan Aarnes, Edward George Effros and Ole A. Nielsen

Vol. 34 (1970), No. 1, 1ā€“16

Let X be a topological space which is second countable, locally compact, and T0. Fell has defined a compact Hausdorff topology on the collection 𝒞(X)) of closed subsets of X. X may be identified with a subset of 𝒞(X), and in the first part of this paper, the original topology on X is related to that induced from 𝒞(X). The main result is a necessary and sufficient condition for X to be almost strongly separated. In the second part, these results are applied to the primitive ideaI space Prim (A) of a separable C-algebra A, giving in particular a necessary and sufficient condition for Prim (A) to be almost separated. Further information concerning ideals in A which are central as C-algebras is obtained.

Mathematical Subject Classification
Primary: 46.65
Received: 11 September 1969
Published: 1 July 1970
Johan Aarnes
Edward George Effros
Ole A. Nielsen