Problem 2

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Topological Rokhlin's Theorem.

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For diffeomorphisms of a

For diffeomorphisms of a compact manifold, see the topological tower theorem in

C. Bonatti and S. Crovisier, Récurrence et généricité. Inventiones Mathematicae 158 (2004), 33–104.

This has been generalized to homeomorphisms on a space with finite dimension in

Y. Gutman, Mean dimension and Jaworski-type theorems. Proc. Lond. Math. Soc. 111 (2015), 831–850.

$Rufus^\infty$

$Rufus^\infty$