(Created page with "=='''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 transform...") |
|||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
=='''Normed Vector Space:'''== | =='''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, ||.||). | + | 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.png|300px|thumbnail|center|Image by Jhausauer]] | ||
Latest revision as of 00:02, 7 December 2020
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.
