Connected ordered topological semigroups with idempotent endpoints. II.

Metrizability of Topological Semigroups on Linearly Ordered Topological Spaces

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...

Idempotent Measures on Compact Semigroups

Throughout this paper, 5 will be a compact Hausdorff topological semigroup, 5 will denote the convolution semigroup of normalized non-negative regular Borel measures on 5, and H will be the carrier of a measure p in 5. The space of continuous complex valued functions on 5 will be denoted by C(S), while Cr(S) will be the subspace of C(S) of real valued functions. Standard terminology and definit...

On supermatrix idempotent operator semigroups

One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives additional to exponential solution to the initial Cauchy problem. The corresponding functional equation and analog of r...

On Maximal Ideals of Compact Connected Topological Semigroups

Definition 1.1. A topological semigroup is a topological space S together with a continuous function m : S × S → S such that S is Hausdorff andm is associative. A subsemigroup of a semigroup S is a nonvoid set A ⊂ S such that A2 ⊂ A, and A is called a subgroup of S if it is a group with respect tom. An element e of a topological semigroup S is called an idempotent if e2 e. Similarly, an element...

Ordered Categories and Ordered Semigroups