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Diffgeom β

Equicontinuous family of functions

Definition

Let F be a family of functions from a topological space X to a metric space Y. Then we say that the functions are equicontinuous if given any x \in X, and any \epsilon \in \R^+, there is an open set U \ni x such that d(f(x),f(x')) < \epsilon \forall x\ \in U, f \in F.