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Needs:
Metrics
Norms
Needed by:
Complete Normed Spaces
Complex Distance
Topological Vector Spaces
Links:
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Norm Metrics

Why

If we have a norm, then we have a metric.

Motivating result

Let $(V, F)$ be a vector space. Let $f: V \to \R $ be a norm. Let $g: V \times V \to \R $ such that

\[ g(x, y) = \norm{x - y}. \]

Then $g$ is a metric.1

  1. Future editions will include an account. ↩︎
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