Normed Vector Spaces
Definition
Metric from Norm
Every normed space is a metric space with this metric.
Examples
Example 1: with norms: for
Example 2: with norm:
Example 3: with (sup norm)
Example 4: with
Unit Ball
Bounded Linear Operators
Properties
Equivalent Norms
Dual Space
Examples of Dual Spaces
Hahn-Banach Theorem
Completion
The completion of a normed space is a Banach space.