Vol. 64, No. 2, 1976

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The extremal structure of locally compact convex sets

J. C. Hankins and Roy Martin Rakestraw

Vol. 64 (1976), No. 2, 413–418

Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases.

Mathematical Subject Classification 2000
Primary: 46A99
Received: 4 August 1975
Revised: 3 November 1975
Published: 1 June 1976
J. C. Hankins
Roy Martin Rakestraw