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The 61 pages that link to Metric space, each with the reason it gives.

• Gromov's compactness theoremNarrower topic: The theorem concerns spaces whose geometry is encoded by distances.

• Kirszbraun theoremNarrower topic: Metric distance defines the Lipschitz condition being preserved.

• Kolmogorov continuity theoremNarrower topic: Distances between parameter values determine the scale in the increment bound.

• Mazur–Ulam theoremNarrower topic: An isometry is defined through distances, even though the theorem’s spaces also have vector operations.

• Skorokhod representation theoremNarrower topic: Polish spaces are complete separable metric spaces, fixing the theorem's ambient setting.

• Vitali covering lemmaNarrower topic: Many formulations use metric balls as the sets being selected and enlarged.

• Johnson–Lindenstrauss lemmaNarrower topic: The theorem begins with points and distances, then places the finite set in Euclidean coordinates.

• Caristi fixed-point theoremNarrower topic: The theorem measures each point’s displacement using a metric.

• Geometry (configuration)Narrower topic: It generalizes geometric configurations to settings defined by distance alone.

• Pompeiu's theoremNarrower topic: The theorem's distance argument relies on a property shared by all metric spaces.

• Two-dimensional spaceRelated: A metric adds measurable distances to points in a two-dimensional space.