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Über Quotienten vollständiger topologischer Vektorräume

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Abstract

The following theorem is proved: Every topological vector space is a quotient of a complete separated topological vector space, in which every bounded set has a finite dimensional linear span.

This improves a result in a former paper of the author [1], in which the above statement has been proved for locally convex spaces.

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Literatur

  1. DIEROLF, S.: Über assoziierte lineare und lokalkonvexe Topologien. To appear in manuscripta math.

  2. IYAHEN, S.O.: On certain classes of linear topological spaces. Proc. London Math. Soc.18, 285–307 (1968).

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  3. KÖHN, J.: Induktive Limiten nicht lokalkonvexer topologischer Vektorräume. Math. Ann.181, 269–278 (1969).

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  4. WAELBROECK, L.: Topological Vector Spaces and Algebras. Lecture Notes in Mathematics, Berlin-Heidelberg-New-York: Springer-Verlag 1971.

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Authors and Affiliations

  1. Math.Inst.der Universität München, Theresienstraße 39, 8 München 2

    Susanne Dierolf

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  1. Susanne Dierolf
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Dierolf, S. Über Quotienten vollständiger topologischer Vektorräume. Manuscripta Math 17, 73–77 (1975). https://doi.org/10.1007/BF01154284

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  • DOI: https://doi.org/10.1007/BF01154284

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