Normed Vector Space:
To get closer to the subject of Banach spaces, we now turn the concept of norms into a usable dimensional space. This product of this transformation is called a normed vector space. A normed vector space is a space represented by the pair (V, ||.||). This space is a type of metric space, which itself is a subset of topological spaces, as seen in the image below.
File:Spaces
Image by Jhausauer
