On continuous linear operators extending metrics

Stasyuk, I.; Tymchatyn, E.

doi:10.1090/S0002-9939-2013-11547-9

On continuous linear operators extending metrics
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by I. Stasyuk and E. D. Tymchatyn PDF

Proc. Amer. Math. Soc. 141 (2013), 2913-2921 Request permission

Abstract:

Let $(X,d)$ be a complete metric space. We prove that there is a continuous, linear extension operator from the space of all partial, continuous, bounded metrics with closed, bounded domains in $X$ endowed with the Hausdorff metric topology to the space of all continuous, bounded, metrics on $X$ with the topology of uniform convergence on compact sets. This is a variant of the result of Tymchatyn and Zarichnyi for continuous metrics defined on closed, variable domains in a compact metric space. We get a similar result for the case of continuous real-valued functions.

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