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.


Image by Jhausauer

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett