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Topology

Metric space

A metric space $(X, d)$ is a set $X$ with a distance function or metric $d$, so that for any $x, y, z \in X$,

  1. d(x, y)=0 iff x=y.
  2. d(x) is non-negative.
  3. d(x, y)=d(y, x).
  4. d(x, y)+d(y, z) ≤ d(x, z). Triangle inequality.