Topological mixing ($\forall U,V\ne \varnothing \exists N\forall n\ge N:F^n(U)\cap V\ne \varnothing$)

A continuous map $F:X\to X$ is 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 mixing.