Definition:Congruence (Metric Spaces)
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This page is about Congruence in the context of Metric Spaces. For other uses, see Congruence.
Definition
Let $\struct {X, d}$ be a metric space.
Two subsets $A, B \subseteq X$ of $X$ are said to be congruent if and only if there exists an isometry $f: X \to X$ such that $\map {f^\to} A = B$.
Such an isometry is called a congruence.
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