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\(\sigma\)-porosity in monotonic analysis with applications to optimization. (English) Zbl 1102.46016

Summary: We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are \(\sigma\)-porous in corresponding spaces. Some applications to optimization are given.

MSC:

46B40 Ordered normed spaces
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
54E52 Baire category, Baire spaces
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