Explore: Lipschitz Spaces

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

In mathematics, a Lipschitz domain (or domain with Lipschitz boundary) is a domain in Euclidean space whose boundary is "sufficiently regular" in the

completeness, as well as uniform, Lipschitz, and Hölder continuity, can be defined in the setting of metric spaces. Other notions, such as continuity

subset of some Hilbert space H1, and H2 is another Hilbert space, and f : U → H 2 {\displaystyle f:U\rightarrow H_{2}} is a Lipschitz-continuous map, then

metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded

category of metric spaces, Met. Such functions are always continuous functions. They are also called Lipschitz functions with Lipschitz constant 1, nonexpansive

vector spaces in the above, and many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and Banach

differential equations exist in appropriate Sobolev spaces, even when there are no strong solutions in spaces of continuous functions with the derivatives understood

isomorphic as vector spaces, but with different multiplications (in the case of characteristic two, they are still isomorphic as vector spaces, just not naturally)

Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard, Ernst Lindelöf, Rudolf Lipschitz and Augustin-Louis