FK-space

Summary

An FK-space is a sequence space with a complete metrizable locally convex topology in which each coordinate $x \mapsto x_n$ is continuous. The letters stand for Fréchet and the German word Koordinate. FK-spaces are the main tool of the functional analytic approach to summability: the domain of a matrix summability method is an FK-space. A sequence space carries at most one FK topology, and inclusions between FK-spaces are automatically continuous.