A note on the Dugundji extension theorem

Lutzer, D.; Martin, H.

doi:10.1090/S0002-9939-1974-0345058-8

A note on the Dugundji extension theorem
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by D. Lutzer and H. Martin

Proc. Amer. Math. Soc. 45 (1974), 137-139

DOI: https://doi.org/10.1090/S0002-9939-1974-0345058-8

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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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