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. © 1976 Pacific Journal of Mathematics. All rights reserved.
J. C. Hankins and R. M. Rakestraw, "The Extremal Structure Of Locally Compact Convex Sets," Pacific Journal of Mathematics, vol. 64, no. 2, pp. 413 - 418, Mathematical Sciences Publishers (MSP), Jan 1976.
The definitive version is available at https://doi.org/10.2140/pjm.1976.64.413
Mathematics and Statistics
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01 Jan 1976