5. Normal spaces. Banach spaces
In elementary geometry, the norm of a vector is defined as its length. Vector calculus extends easily to very general functional spaces, and it's useful to be able to use the notion of norm of a function, an operator, a linear form... The structure of normed space that we're now defining is fundamental when we want to apply geometric ideas to analysis.
Definition 1: Let E be a vector space. A normN on E is an application that verifies the following...
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Normal spaces. Banach spaces
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