Vol. 20, No. 1, 1967

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A topological characterization of Gleason parts

John Brady Garnett

Vol. 20 (1967), No. 1, 59–63

Let A be a function algebra on its maximal ideal space M(A), and let P be a Gleason part of M(A). It is easily seen that P is then a σ-compact completely regular space. We prove the converse: if K is completely regular and σ-compact, then there exists a function algebra whose maximal ideal space contains a part homeomorphic to K. Every bounded continuous function on that part is the restriction of a function in the given algebra. Consequently no subset of the part can have an analytic structure.

Mathematical Subject Classification
Primary: 46.55
Received: 12 January 1966
Published: 1 January 1967
John Brady Garnett
Department of Mathematics
University of California
Los Angeles CA 90024
United States