Extending Lipschitz mappings continuously
Eva Kopecká · Journal of Applied Analysis · 2012
We consider short mappings from a bounded subset of a Euclidean space into that space, that is, mappings which do not increase distances between points. By Kirszbraun's theorem any such mapping can be extended to the entire space to be short again. In general, the extension is not unique. We show that there are single-valued extension operators continuous in the supremum norm. The multivalued extension operator is lower semicontinuous.