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Published online by Cambridge University Press: 31 January 2025
2.1 Definitions and Examples
We now introduce the fundamental object in our investigations. A vector space, while very useful, is somewhat unwieldy when it is infinite dimensional. Equipping it with a metric, especially one that understands the linear structure of the underlying set, is a simple and effective way to alleviate this problem.
2.1.1 DEFINITION A norm on a K-vector space E is a function
which satisfies the following properties for all x, y ∊ E and all α ∊ K.
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