Embeddings of compact convex sets and locally compact cones
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. © 1976, University of California, Berkeley. All Rights Reserved.
Publication Source (Journal or Book title)
Pacific Journal of Mathematics
Lawson, J. (1976). Embeddings of compact convex sets and locally compact cones. Pacific Journal of Mathematics, 66 (2), 443-453. https://doi.org/10.2140/pjm.1976.66.443