Answer to Question #1035 in Complex Analysis for Tashu

Question

Give the definition of Banach spaces and explain why this notion is important only when
working with infinite dimensional vector spaces.

Answer 1

Banach space is a complete normed vector space. This means that a Banach space is a vector space V over the real or complex numbers with the defined norm, so that any fundamental sequence in V has a limit, which also belongs to V.