Vol. 17, No. 1, 1966

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Exposed points of convex sets

Gustave Choquet, Harry Corson and Victor Klee

Vol. 17 (1966), No. 1, 33–43

The two sections of this note are unrelated, except that both are concerned with the exposed points of a compact convex subset K of a locally convex space E. In §1 it is proved that if K is of finite dimension d, then the set of all its exposed points can be expressed as the union of a Gδ set, an Fσ set, and d 2 sets each of which is the intersection of a Gδ set with an Fσ set. A sharper assertion is proved for the three-dimensional case, and some related results are obtained for certain infinite-dimensional situations. Section 2 describes a compact convex set in the space Rc which has no algebraically exposed points. Both sections contain unsolved problems.

Mathematical Subject Classification
Primary: 46.01
Secondary: 52.30
Received: 5 November 1964
Published: 1 April 1966
Gustave Choquet
Harry Corson
Victor Klee
University of Washington
United States