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Induktive und projektive Limiten mit Zerlegung der Einheit

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Abstract

Inductive and projective limits with partition of unity were introduced and investigated in M. De Wilde [1]. In this note we show that these spaces are complemented subspaces of certain direct sums and products. Especially the function spaceD(Ω) is a complemented subspace of\(\mathop \oplus \limits_{\text{n}}\) D(Kn). Because of this property of these spaces the results in [1] are easy consequences of corresponding results for direct sums and products.

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Literatur

  1. DE WILDE, M.: Inductive limits and partitions of unity. Manuscripta math. 5, 45–58 (1971).

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  2. KÖTHE, G.: Topologische lineare Räume I. Berlin-Heidelberg-New York: Springer 1966.

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Authors and Affiliations

  1. Math. Seminar der Universität 6, Robert-Mayer-Str. 10, Frankfurt/M., Germany

    Dieter Keim

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  1. Dieter Keim
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Keim, D. Induktive und projektive Limiten mit Zerlegung der Einheit. Manuscripta Math 10, 191–195 (1973). https://doi.org/10.1007/BF01475041

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  • DOI: https://doi.org/10.1007/BF01475041

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