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Metric space

Set

context $X$ … set
definiendum $\langle X,d\rangle\in\mathrm{it}$
postulate $d\in$ metric $X$

Discussion

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: Metric space

Parents

Refinement of

Requirements*

Equivalent to

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