In mathematics, a Fréchet surface is an equivalence class of parametrized surfaces in a metric space.
In other words, a Fréchet surface is a way of thinking about surfaces independently of how they are "written down" (parametrized).
The concept is named after the French mathematician Maurice Fréchet.
be a compact 2-dimensional manifold, either closed or with boundary, and let
A parametrized surface in
that is continuous with respect to the topology on
Call two parametrized surfaces
of parametrized surfaces under this notion of equivalence is called a Fréchet surface; each of the parametrized surfaces in this equivalence class is called a parametrization of the Fréchet surface
Many properties of parametrized surfaces are actually properties of the Fréchet surface, that is, of the whole equivalence class, and not of any particular parametrization.
For example, given two Fréchet surfaces, the value of
is independent of the choice of the parametrizations
and is called the Fréchet distance between the Fréchet surfaces.
This metric geometry-related article is a stub.