Separable reduction of local metric regularity

Fabian, M.; Ioffe, A.; Revalski, J.

doi:10.1090/proc/14071

Separable reduction of local metric regularity
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by M. Fabian, A. D. Ioffe and J. Revalski

Proc. Amer. Math. Soc. 146 (2018), 5157-5167

DOI: https://doi.org/10.1090/proc/14071

Published electronically: September 10, 2018

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Abstract:

We prove that the property of a set-valued mapping $F:X \rightrightarrows Y$ to be locally metrically regular (and consequently, the properties of the mapping to be linearly open or pseudo-Lipschitz) is separably reducible by rich families of separable subspaces of $X\times Y$. In fact, we prove that, moreover, this extends to computation of the functor $\textrm {{reg}} F$ that associates with $F$ the rates of local metric regularity of $F$ near points of its graph.

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