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Displaying 101 – 120 of 196

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The universal minimal system for the group of homeomorphisms of the Cantor set

E. Glasner, B. Weiss (2003)

Fundamenta Mathematicae

Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact noncompact group this is a nonmetrizable system with a rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one-point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizable space and for which one has an explicit description. We show that for the topological group G = Homeo(E) of self-homeomorphisms...

The σ-ideal of closed smooth sets does not have the covering property

Carlos Uzcátegui (1996)

Fundamenta Mathematicae

We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.

Theorem on signatures

Władysław Kulpa, Andrzej Szymański (2007)

Acta Universitatis Carolinae. Mathematica et Physica

Currently displaying 101 – 120 of 196