Fréchet

Fréchet is a French surname associated with several key concepts in mathematics, most notably through the work of Maurice Fréchet (1878–1973), a French mathematician who helped establish modern topology and functional analysis. His contributions laid the foundations for topology, analysis in infinite-dimensional spaces, and metric geometry, influencing many areas of mathematical analysis.

In mathematics, several notions bear his name. The Fréchet derivative generalizes the derivative for mappings between normed spaces: a function f is Fréchet differentiable at a point if there exists a bounded linear operator that provides a first-order linear approximation to f near that point. A Fréchet space is a locally convex, complete, metrizable topological vector space, extending Banach spaces by dropping the requirement of a single norm. The Fréchet distance measures similarity between curves by considering their continuous reparameterizations, effectively the minimal leash length needed for a walker and a dog to traverse the curves in sync. The Fréchet mean is the minimizer of the expected squared distance to a random variable in a metric space, a generalization of the ordinary mean to non-Euclidean settings. The Fréchet distribution is a heavy-tailed extreme value distribution used to model the maximum of samples, with support on the positive real line. The Fréchet inequalities, or Fréchet bounds, provide the tightest possible bounds on a joint distribution given fixed marginals, a foundational result in probability theory.