Separable Reduction of Metric Regularity Properties
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.
KeywordsSet-valued mapping Linear openness Metric regularity Regularity rates Separable reduction
I wish to thank the reviewers for valuable comments and many helpful remarks.
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