Lipschitz Algebras and Lipschitz-Free Spaces Over Unbounded Metric Spaces
Lipschitz Algebras and Lipschitz-Free Spaces Over Unbounded Metric Spaces
Abstract We investigate a way to turn an arbitrary (usually, unbounded) metric space ${{\mathcal{M}}}$ into a bounded metric space ${{\mathcal{B}}}$ in such a way that the corresponding Lipschitz-free spaces ${{\mathcal{F}}}({{\mathcal{M}}})$ and ${{\mathcal{F}}}({{\mathcal{B}}})$ are isomorphic. The construction we provide is functorial in a weak sense and has the advantage of being …