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Proceedings of the American Mathematical Society

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



Approximation of vector-valued continuous functions

Author: Alan H. Shuchat
Journal: Proc. Amer. Math. Soc. 31 (1972), 97-103
MathSciNet review: 0290082
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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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Keywords: Topological vector spaces, vector-valued continuous functions, vector measures, extension of vector-valued functions
Article copyright: © Copyright 1972 American Mathematical Society