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We study dynamics of continuous maps on compact metrizable spaces containinga free interval (i.e., an open subset homeomorphic to an open interval). Aspecial attention is paid to relationships between topological transitivity,weak and strong topological mixing, dense periodicity and topological entropyas well as to the topological structure of minimal sets. In particular, atrichotomy for minimal sets and a dichotomy for transitive maps are proved.

Dynamical consequences of a free interval: minimality, transitivity, mixing and topological entropy