===== Metric space =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ ...  set |
| @#FFBB00: definiendum | @#FFBB00: $\langle X,d\rangle\in\mathrm{it}$ |
| @#55EE55: postulate   | @#55EE55: $d$ ... metric $X$ |

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We can reconstruct the set underlying a metric via $\text{dom}(\text{dom}(d))=\text{dom}(X\times X)=X$, so the set of metrics and the set of metric spaces over $X$ are in bijection.
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Metric_space|Metric space]]

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=== Requirements* ===
[[Metric]]
=== Refinement of ===
[[Hausdorff space]]
=== Equivalent to ===
[[Metric]]