Banach space

A Banach space is a type of vector space, which is a space made up of vectors. In a Banach space, the length and distance between vectors can be calculated. It is also complete, meaning that a Cauchy sequence of vectors will always reach a limit. The concept was created and studied by Polish mathematician Stefan Banach in 1920-1922. The term "Banach space" was first used by Maurice René Fréchet, and Banach coined the term "Fréchet space". Banach spaces come from the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century, and play an important role in functional analysis.