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Metric Space

Last updated Nov 1, 2022

# Definition

A Metric Space is a Set $M$ equipped with a Distance Function $d: M \times M \to \mathbb{R}_{\geq0}$.

# Remarks

  1. A Metric Space is naturally endowed with the Metric Topology
  2. An Extended Metric Space is a Metric Space if its Extended Distance Function is actually a Distance Function