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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. | 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|thumbnail|center|Image by Jhausauer]] | + | [[File:Spaces.png|thumbnail|center|Image by Jhausauer]] |
Revision as of 22:19, 6 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.
