Continuous linear extension of functions

Koyama, A.; Stasyuk, I.; Tymchatyn, E.; Zagorodnyuk, A.

doi:10.1090/S0002-9939-2010-10424-0

Continuous linear extension of functions
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by A. Koyama, I. Stasyuk, E. D. Tymchatyn and A. Zagorodnyuk PDF

Proc. Amer. Math. Soc. 138 (2010), 4149-4155 Request permission

Abstract:

Let $(X,d)$ be a complete metric space. We prove that there is a continuous, linear, regular extension operator from the space $C^*_b$ of all partial, continuous, real-valued, bounded functions with closed, bounded domains in $X$ to the space $C^*(X)$ of all continuous, bounded, real-valued functions on $X$ with the topology of uniform convergence on compact sets. This is a variant of a result of Kunzi and Shapiro for continuous functions with compact, variable domains.

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