Compact convex sets in 2-dimensional asymmetric normed lattices

2014/03/27 by Natalia Jonard-Pérez, Jonard-Pérez, Natalia, Enrique A. Sánchez-Pérez +1
Mathematics · #46A50 #46A55 #46B50 #52A07 #52A10 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #math.FA #math.GN #msc:46A50 #msc:46A55 #msc:46B50 #msc:52A07 #msc:52A10

paper · pdf · doi:10.48550/arxiv.1403.6986

arxiv created 2014/09/09 · arxiv updated 2014/09/10

Abstract

We study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric description of the compact convex sets with non empty interior in (R², q), where q is an asymmetric lattice norm.

Related

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• Local compactness in right bounded asymmetric normed spaces
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• On compact sets possessing q-convex functions
• Local convexity in CAT(κ)-spaces