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Topological groups with Rokhlin properties

Eli Glasner, Benjamin Weiss (2008)

Colloquium Mathematicae

In his classical paper [Ann. of Math. 45 (1944)] P. R. Halmos shows that weak mixing is generic in the measure preserving transformations. Later, in his book, Lectures on Ergodic Theory, he gave a more streamlined proof of this fact based on a fundamental lemma due to V. A. Rokhlin. For this reason the name of Rokhlin has been attached to a variety of results, old and new, relating to the density of conjugacy classes in topological groups. In this paper we will survey some of the new developments...

Trajectories, first return limiting notions and rings of H -connected and iteratively H -connected functions

Ewa Korczak-Kubiak, Ryszard J. Pawlak (2013)

Czechoslovak Mathematical Journal

In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted C o n n * ) contained between the families (widely described in literature) of Darboux Baire 1 functions ( DB 1 ) and connectivity functions ( C o n n ). The solutions to our problems are based, among other, on the suitable construction of the ring,...

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