Fréchet space

In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). Fréchet spaces are locally convex spaces that are complete with respect to a translation invariant metric. In contrast to Banach spaces, the metric need not arise from a norm.