# Banach Space

A Banach space is a vector space that has a complete norm. Banach spaces are important in the study of infinite-dimensional vector spaces.

Banach space is a college-level concept that would be first encountered in an analysis course covering functional analysis.

### Prerequisites

Norm: | A norm is a quantity that describes the length, size, or extent of a mathematical object. |

Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |