Open AccessSeparable reduction of local metric regularity
Author(s) -
Marián Fabian,
A. D. Ioffe,
Julian P. Revalski
Publication year - 2018
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14071
Subject(s) - algorithm , computer science , artificial intelligence , annotation , separable space , mathematics , mathematical analysis
We prove that the property of a set-valued mapping F : X ⇉ Y 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 × Y X\times Y . In fact, we prove that, moreover, this extends to computation of the functor {reg} F \textrm {{reg}}\, F that associates with F F the rates of local metric regularity of F F near points of its graph.