Furstenberg families and sensitivity.
Equicontinuity, shadowing and distality in general topological spaces
We consider the notions of equicontinuity point, sensitivity point and so on from a topological point of view. Many of these notions can be sensibly defined either in terms of (finite) open covers or uniformities. We show that for the notions of equicontinuity point and sensitivity point, Hausdorff or uniform versions coincide in compact Hausdorff spaces and are equivalent to the standard definitions stated in terms of a metric in compact metric spaces. We prove that a uniformly chain transitive...
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