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Further arguments for slice convergence in nonreflexive spaces

Borwein, Jonathan M. and Vanderwerff, Jon D. (1994) Further arguments for slice convergence in nonreflexive spaces. Set-Valued Analysis, 2 (4). pp. 529-544. ISSN 0927-6947

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      Abstract

      It is shown that no notion of set convergence at least as strong as Wijsman convergence but not as strong as slice convergence can be preserved in superspaces. We also show that such intermediate notions of convergence do not always admit representations analogous to those given by Attouch and Beer for slice convergence, and provide a valid reformulation. Some connections between bornologies and the relationships between certain gap convergences for nonconvex sets are also observed.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: set convergence, convexity, Kadec-Klee norms, Mosco convergence, slice convergence, Wijsman convergence
      Subjects: 46-xx Functional analysis > 46Axx Topological linear spaces and related structures
      40-xx Sequences, series, summability > 40Axx Convergence and divergence of infinite limiting processes
      46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 16 Nov 2003
      Last Modified: 07 Sep 2014 20:04
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/62

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