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Topological AE(0)-groups

Alex Chigogidze (2001)

Fundamenta Mathematicae

We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group S is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product...

Topological aspects of infinitude of primes in arithmetic progressions

František Marko, Štefan Porubský (2015)

Colloquium Mathematicae

We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (1997), and correct some results from that paper. Then we determine cluster...

Topological automorphism groups of chains.

Sergei V. Ovchinnikov (2001)

Mathware and Soft Computing

It is shown that any set-open topology on the automorphism group A(X) of a chain X coincides with the pointwise topology and that A(X) is a topological group with respect to this topology. Topological properties of connectedness and compactness in A(X) are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.

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...

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