We know that if S is a subsemigroup of a semitopological semigroup T , and stands for one of the spaces , , , or , and ( ,T ) denotes the canonical -compactification of T , where T has the property that (S) = (T)|s , then ( |s , (S)) is an -compactification of S. In this paper, we try to show the converse of this problem when T is a locally compact group and S is a closed normal subgroup of T ....

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

We call a semigroup compactification T of a (discrete) semigroup S Boolean if the underlying space of T is zero-dimensional. The class of Boolean compactifications of S is a complete lattice, in a natural way. Motivated by Numakura’s theoerem, we prove that this lattice is isomorphic to the ideal lattice of the lattice of finite congruence relations of S. We describe in some detail the lattice ...

We propose a definition of a “C-Eberlein” algebra, which is a weak form of a C-bialgebra with a sort of “unitary generator”. Our definition is motivated to ensure that commutative examples arise exactly from semigroups of contractions on a Hilbert space, as extensively studied recently by Spronk and Stokke. The terminology arises as the Eberlein algebra, the uniform closure of the Fourier-Stiel...

The Stone-Čech compactification of discrete semigroups is a tool of central importance in several areas of mathematics, and has been studied extensively. We think of the Stone-Čech compactification of a discrete abelian semigroup G as the set βG of ultrafilters on G, where the point x ∈ G is identified with the principal ultrafilter {A ⊆ G ∣∣x ∈ A}, and the basic open sets are those of the form...

For G a group definable in some structure M , we define notions of “definable” compactification of G and “definable” action of G on a compact space X (definable G-flow), where the latter is under a definability of types assumption on M . We describe the universal definable compactification of G as G∗/(G∗)00 M and the universal definable G-ambit as the type space SG(M). We also point out the exi...