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Mosco convergence and weak topologies for convex sets and functions
Author(s) -
Beer Gerald
Publication year - 1991
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006471
Subject(s) - mathematics , weak topology (polar topology) , banach space , uniformly convex space , weak convergence , reflexive space , convex function , locally convex topological vector space , convergence (economics) , convex set , topology (electrical circuits) , regular polygon , discrete mathematics , pure mathematics , topological space , general topology , combinatorics , extension topology , interpolation space , eberlein–šmulian theorem , convex optimization , functional analysis , lp space , geometry , computer security , asset (computer security) , economic growth , chemistry , computer science , biochemistry , economics , gene
Let X be a reflexive Banach space. This article presents a number of new characterizations of the topology of Mosco convergence TM for convex sets and functions in terms of natural geometric operators and functional. In addition, necessary and sufficient conditions are given for TM to agree with the weak topology generated by { d ( x , C ): x є X }, where each distance functional is viewed as a function of the set argument.