Boolean lattices of function algebras on rectangular semigroups.
We calculate the cardinal characteristics of the -ideal of Haar null subsets of a Polish non-locally compact group with invariant metric and show that . If is the product of abelian locally compact groups , then , , and , where is the ideal of Lebesgue null subsets on the real line. Martin Axiom implies that and hence contains a Haar null subset that cannot be enlarged to a Borel or projective Haar null subset of . This gives a negative (consistent) answer to a question of...
In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.
Let be the wreath product of a compact group T with the infinite symmetric group . We study the characters of factor representations of finite type of G, and give a formula which expresses all the characters explicitly.
For extending the notion of -algebra, as defined in [2], we present an example of an m-admissible algebra which is not an - algebra. Then we define -subcompactification and -subcompactification to study the universal -subcompactification and the universal -subcompactification from the function algebras point of view.
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of . Other results on subgroups of linear spaces are obtained.