A topological semigroup is a nonvoid, Hausdorff space, 5, together with a continuous, associative multiplication defined on 5. Here the term semigroup will always denote a topological semigroup. In [4], Wallace and Koch have shown that if the circle, B, is a semigroup such that B2 = B, then either B is a group, or the multiplication on B is of the trivial kind xy = x, or xy = y. In [6], Mostert...

Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the semigroup is contained in an ambit. In the convolution algebras constructed over ambitable semigroups, topological centres have a tractable characterization. 1...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...

We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. 1. Definition of the cohomology Bounded cohomology was first defined for discrete groups by F. Trauber and then for topological spaces by M. Gromov [6]. In this paper we establish a topological bounded co...

The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier ...

Here a typical topological semigroup C(G) is studied. A partial equivalence [1] is defined on C(G) compatible with its semigroup structure. Also a uniformity is constructed giving the Vietoris topology [3] on C(G).