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manuscripta mathematica

, Volume 14, Issue 2, pp 107–121 | Cite as

Tonneliertheit in lokalkonvexen Vektorgruppen

  • Pawel Lurje
Article

Abstract

Locally convex vector groups are topological vector spaces over the discrete real or complex numberfield with a neighbourhoodbase of zero consisting of absolutely convex sets (cf. P. Kenderov [3], D.A. Raikov [8]). In this note, which is a continuation of “Lokalkreisförmige Vektorgruppen” (to appear in this journal), we introduce the concept of barrelled locally convex vector groups, study their permanence properties under the usual constructions (final-initialtopologies etc.) and prove the principle of uniform boundedness in this setting. Finally we consider some special examples of barrelled locally convex vector groups leading to a generalisation of a theorem of V. Ptak (Theorem 2.2 in [7]), which turns out to be a special case of the uniform boundedness principle for locally convex vector groups.

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Literatur

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Pawel Lurje
    • 1
  1. 1.München 40

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