Mappings on the dyadic solenoid
Answering an open problem in [3] we show that for an even number , there exist no to mappings on the dyadic solenoid.
Means of translates
Metrization criteria for compact groups in terms of their dense subgroups
According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...
Minimal Topological Groups.
Nearly disjoint sequences in convergence -groups
For an abelian lattice ordered group let be the system of all compatible convergences on ; this system is a meet semilattice but in general it fails to be a lattice. Let be the convergence on which is generated by the set of all nearly disjoint sequences in , and let be any element of . In the present paper we prove that the join does exist in .
Near-rings of continuous functions on compact abelian groups.
Non-archimedean induced representations of compact zerodimensional groups
Non-archimedean representations of compact groups
Noncompact semigroup actions.
On a centralizer result of Hunter's (correspondence between Karl Heinrich Hofmann and Robert P. Hunter).
On a covering group theorem and its applications.
On additive number-theoretical functions with values in a compact Abelian group.
On averages of randomized class functions on the symmetric groups and their asymptotics
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...
On certain two generator monoids.
On Exact Toral Endomorphisms.
On iterated limits of subsets of a convergence -group
In this paper we deal with the relation for a subset of , where is an -group and is a sequential convergence on .
On normal subgroups of compact groups
Among compact Hausdorff groups whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup is closed for every closed normal subgroup of .
On projective and injective objects of the categories dual to .
On the decomposition of Haar measure in compact groups
On the density character of compact topological groups