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Über beschränkte Mengen in induktiven Limiten topologischer Vektorräume

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Abstract

In topological linear spaces convex hulls of bounded sets are, in general, not bounded. The question arises whether there is at least for every bounded set B a sequence {λν|νεℕ} of strictly positive numbers such that the set ∪{Σ nl λ v B|nεℕ} is bounded. When this obtains, bounded sets share several of the properties known in locally convex spaces. The main result of this note is an example of a countable inductive limit of complete metrizable topological linear spaces which is neither regular nor sequentially complete and also fails to have the above “bounded summability property”.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Wegelerstraße 10, 5300, Bonn, Bundesrepublik Deutschland

    Wolfgang Ruess

  2. Fachbereich 17 Gesamthochschule Pohlweg 47-49, 4790, Paderborn, Bundesrepublik Deutschland

    Robert Wagner

Authors
  1. Wolfgang Ruess
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  2. Robert Wagner
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Ruess, W., Wagner, R. Über beschränkte Mengen in induktiven Limiten topologischer Vektorräume. Manuscripta Math 19, 365–374 (1976). https://doi.org/10.1007/BF01278924

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  • DOI: https://doi.org/10.1007/BF01278924

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