A flow is called equicontinuous if the collection of maps defined by the action of the group is a uniformly equicontinuous family.

Formally, a flow \((X,T)\) is equicontinuous if for any open \(U \subseteq X\), there is an open \(V \subseteq X\) such that whenever \((x,x') \in V\), then \((xt, x't) \in U\), for all \(t \in T\).

More succinctly, if open \(U \subseteq X\), there is a \(V \subseteq X\) such that \(VT \subseteq U\).

• Equicontinuous extension