Definition:Distance/Points/Normed Vector Space
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Definition
Let $\struct {X, \norm {\, \cdot \,}}$ be a normed vector space.
Let $x, y \in X$ .
Then the function $\norm {\, \cdot \,} : X \times X \to \R$:
- $\map d {x, y} = \norm {x - y}$
is called the distance between $x$ and $y$.
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): $\S 1.2$: Normed and Banach spaces. Normed spaces