Separable Reduction of Metric Regularity Properties

A. D. Ioffe ()
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A. D. Ioffe: Department of Mathematics, Technion

A chapter in Constructive Nonsmooth Analysis and Related Topics, 2014, pp 25-37 from Springer

Abstract: Abstract We show that for a set-valued mapping F: X → Y between Banach spaces the property of metric regularity near a point of its graph is separably determined in the sense that it holds, provided for any separable subspaces L 0 ⊂ X and M ⊂ Y, containing the corresponding components of the point, there is a separable subspace L ⊂ X containing L 0 such that the mapping whose graph is the intersection of the graph of F with L × M (restriction of F to L × M) is metrically regular near the same point. Moreover, it is shown that the rates of regularity of the mapping near the point can be recovered from the rates of such restrictions.

Keywords: Set-valued mapping; Linear openness; Metric regularity; Regularity rates; Separable reduction (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-8615-2_3

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DOI: 10.1007/978-1-4614-8615-2_3

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