Vol. 34, No. 1, 1970

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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