On continuous extension of uniformly continuous functions and metrics
Volume 116 / 2009
Colloquium Mathematicum 116 (2009), 191-202
MSC: 54E35, 54C20, 54E40.
DOI: 10.4064/cm116-2-4
Abstract
We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space $(X,d)$. In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
