Topological mixing
= Topological mixing
{title2=$\forall U,V\ne\varnothing\ \exists N\ \forall n\ge N:\ F^n(U)\cap V\ne\varnothing$}
= Topologically mixing
{synonym}
A continuous <discrete dynamical system>[map] $F:X\to X$ is <topological mixing>[topologically mixing] if for every pair of nonempty open sets $U,V$ there is an <integer> $N$ such that $F^n(U)\cap V\ne\varnothing$ for every $n\ge N$. This is stronger than <topological transitivity>, which asks only for some hitting time. For the full <tent map>, each sufficiently small dyadic branch interval is mapped onto the whole space by an iterate, proving <topological mixing>[mixing].