Journal of Convex Analysis 31 (2024), No. 1, 075--110
Copyright Heldermann Verlag 2024
Compactness in Locally Convex Cones
Walter Roth
Tacip Mirafuentes, Tagum City, Davao del Norte, Philippines
walter.roth47@gmail.com
We investigate notions of compactness with respect to the relative topologies of a locally convex cone. Since these topologies are generally not Hausdorff and the uniform structures induced by the upper and lower relative topologies are not symmetric, we introduce suitable generalizations for the concepts of precompactness and completeness, which nonetheless coincide with the usual ones in the symmetric case, that is in particular for the example of locally convex topological vector spaces. Locally compact cones comprise the topic for the final part of this paper.
Keywords: Locally convex cones, compactness, locally compact cones.
MSC: 46A03, 46A50, 54D45, 54E15.
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