Vol. 66, No. 2, 1976

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Embeddings of compact convex sets and locally compact cones

Jimmie Don Lawson

Vol. 66 (1976), No. 2, 443–453

The main result of this paper is that a compact convex set with a basis of neighborhoods (not necessarily open) at each point which are convex can be embedded in a locally convex separated topological vector space. An analogous result is proved for locally compact cones. Along the way it is shown that any compact convex set can be embedded as a base of a locally compact cone in a separated topological vector space, and that the various notions of local convexity coincide in a compact convex set.

Mathematical Subject Classification 2000
Primary: 46A99
Received: 23 December 1975
Revised: 3 August 1976
Published: 1 October 1976
Jimmie Don Lawson