Frechet

Fréchet, often written with the acute accent as Fréchet, is a surname most closely associated with the French mathematician Maurice Fréchet (1878–1973). His work helped lay the foundations of modern topology and functional analysis, and several mathematical concepts bear his name. The spelling Frechet is a common anglicized variant.

Fréchet space is a type of topological vector space that is locally convex, complete, and metrizable. It generalizes Banach spaces and forms an important setting in functional analysis and probability theory, where notions of convergence and continuity can be developed without requiring a norm.

Fréchet derivative extends the classical derivative to functions between Banach spaces. A function is Fréchet differentiable at a point if there exists a bounded linear map that provides a best linear approximation in a neighborhood of that point, with the remainder becoming negligible relative to the input increment.

Fréchet mean, or Fréchet expectation, generalizes the concept of an average to metric spaces. It is the point that minimizes the expected squared distance to random observations, making it applicable in non-Euclidean spaces such as manifolds and graphs.

Fréchet distance measures similarity between curves, accounting for both the spatial alignment and the sequence of points along the curves. Conceptually described by a person and a leash walking along each curve, it is widely used in computer graphics, pattern recognition, and trajectory analysis.

Fréchet distribution is one of the three types of extreme value distributions (Type II) used in modeling the distribution of maxima with heavy tails. It is part of the broader theory of extreme events in statistics.