Banach space definition
There are two common types of Banach space: "real Banach space" and "complex Banach space", which refer to the definition of the vector space of the Banach space on the domain composed of real or complex numbers.
Many infinite-dimensional function spaces learned in mathematical analysis are Banach spaces, including spaces composed of continuous functions (continuous functions on compact Heusdorff spaces), and Lp spaces composed of Lebesgue integrable functions And Hardy space composed of holomorphic functions. The above spaces are the most common types in topological vector spaces, and the topologies of these spaces all come from their norms.
The Banach space is named after the Polish mathematician Stefan Banach, who proposed this space in 1920-1922 with Hans Hahn and Edward Heli.