Countability, Completeness and the Closed Graph Theorem

  • R. Beattie
  • H.-P. Butzmann


The webs of M. De Wilde [4] have made an enormous contribution to the closed graph theorems in locally convex spaces(lcs). Although webs have a very intricate layered construction, two properties in particular have contributed to the closed graph theorem. First of all, webs possess a strong countability condition in the range space which suitably matches the Baire property of Fréchet spaces in the domain space; as a result the zero neighbourhood filter is mapped to a p-Cauchy filter, a filter attempting to settle down. Secondly webs provide a completeness condition which allow p-Cauchy filters to converge.


Countable Basis Closed Graph Graph Theorem Completeness Property Closed Graph Theorem 
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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • R. Beattie
    • 1
  • H.-P. Butzmann
    • 2
  1. 1.Dept. of Mathematics and Computer ScienceMount Allison UniversitySackvilleCanada
  2. 2.Fakultät für Mathematik und InformatikUniversität MannheimMannheimDeutschland

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