When all closed subsets are recurrent?
Abstract
In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. (X,T) and the t.d.s. (K(X),TK) induced on the hyperspace K(X) of all compact subsets of X, and provide some characterizations. Among other examples, we construct a minimal, non-equicontinuous, distal and uniformly rigid t.d.s. and a t.d.s. which has dense small periodic sets but does not have dense distal points, solving that way open questions existing in the literature.
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