I'm working through some old notes on Dynamical systems, and I see a definition that I'm not familiar with. I'll call it property B, because I'm not sure what else to call it. In the notes, we assume we are in a compact metric space $X$.
A dynamical system $T: X \rightarrow X$ has property B if for every non-empty open set $U \subseteq X$, there exists some $n \geq 0$ such that $T^n(U) = X$.
Has anyone ever seen this or used this before? It's evidently stronger than transitivity and mixing, but not minimality.
I seem to have seen this before in a class I took in Ergodic Theory. If I remember right it was called Topologically Exact. But I don't see much when I type that as a google search.