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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximation of vector-valued continuous functions
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by Alan H. Shuchat
Proc. Amer. Math. Soc. 31 (1972), 97-103
DOI: https://doi.org/10.1090/S0002-9939-1972-0290082-5
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Abstract:

The results of this article are important for proving Riesz-type representation theorems for spaces of continuous functions with values in a topological vector space. It is well known that every continuous function with compact support from a locally compact Hausdorff space to a locally convex space can be uniformly approximated by continuous functions with finite-dimensional range. We give several conditions sufficient for this to be true without convexity. This problem is related to a vector-valued Tietze extension problem, and we give a new proof of a theorem of Dugundji, Arens, and Michael in this area, using topological tensor products.
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 97-103
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0290082-5
  • MathSciNet review: 0290082