Topic summary
Lipschitz continuous
Extracted from the Wikipedia article Lipschitz continuity.
Definitions
A function is called locally Lipschitz continuous if for every x in X there exists a neighborhoodU of x such that f restricted to U is Lipschitz continuous. Equivalently, if X is a locally compact metric space, then f is locally Lipschitz if and only if it is Lipschitz continuous on every compact subset of X. In spaces that are not locally compact, this is a necessary but not a sufficient condition.