Almost open semigroup actions.

A dynamical system (X, S, π) is a triplet where X is a metric space, S a topological monoid and π a continuous action of S on X. A dynamical system (X, S, π) is called almost open if int(sW) ̸= ∅ for every open subset W of X (int(sU) denotes the interior of sU). A metric S-system (X, d) is sensitive if it satisfies the condition: there exists a (sensitivy constant) c > 0 such that for all x ∈ X and all δ > 0 there are some y ∈ Bδ(x) and s ∈ S with d(sx, sy) > c. A topological space is called Polish if it admits a separable complete metric. The authors obtain sufficient conditions for the sensitivity of an almost open dynamical system (X, S, π) with X Polish.