Set-Valued Analysis

, Volume 2, Issue 4, pp 529–544 | Cite as

Further arguments for slice convergence in nonreflexive spaces

  • Jon Borwein
  • Jon Vanderwerff


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.

Key words

Set convergence convexity Kadec-Klee norms Mosco convergence slice convergence Wijsman convergence 

Mathematics Subject Classifications (1991)

Primary 46A55. Secondary 46B20 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Jon Borwein
    • 1
  • Jon Vanderwerff
    • 1
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

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