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Separable reduction of local metric regularity

Authors: M. Fabian, A. D. Ioffe and J. Revalski
Journal: Proc. Amer. Math. Soc. 146 (2018), 5157-5167
MSC (2010): Primary 46B26, 47H04, 49J53, 58C06
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 $ {\rm {reg}}\, F$ that associates with $ F$ the rates of local metric regularity of $ F$ near points of its graph.

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Additional Information

M. Fabian
Affiliation: Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

A. D. Ioffe
Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

J. Revalski
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Akad. G. Bonchev str. block 8, 1113 Sofia, Bulgaria

Keywords: Metric space, local metric regularity, metric subregularity, rich family, separable reduction
Received by editor(s): October 21, 2017
Received by editor(s) in revised form: December 21, 2017
Published electronically: September 10, 2018
Additional Notes: The first author was supported by grant GAČR 17–00941S and by RVO: 67985840.
The research of the third author was partly supported by the Bulgarian National Fund for Scientific Research under the grant DFMI I02/10/2014
Dedicated: Dedicated to the memory of our friend and collaborator, Jonathan Michael Borwein
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2018 American Mathematical Society

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