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Proceedings of the American Mathematical Society

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

 

 

A note on the Dugundji extension theorem


Authors: D. Lutzer and H. Martin
Journal: Proc. Amer. Math. Soc. 45 (1974), 137-139
MSC: Primary 54C20
DOI: https://doi.org/10.1090/S0002-9939-1974-0345058-8
MathSciNet review: 0345058
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Abstract: We prove that if $ A$ is a closed, metrizable, $ {G_\delta }$-subspace of a collectionwise normal space $ X$ then there is a linear transformation $ e:C(A) \to C(X)$ such that for each $ g\in C(A),e(g)$ extends $ g$ and the range of $ e(g)$ is contained in the closed convex hull of the range of $ g$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0345058-8
Keywords: Dugundji extension theorem, simultaneous extension of functions, collectionwise normality
Article copyright: © Copyright 1974 American Mathematical Society