Topological Semigroups and their Prequantale Models

Abstract

In this paper, we introduce a Condition ($\Delta$) on topological
semigroups, and prove that every $T_1$ topological semigroup
satisfying Condition ($\Delta$) has a bounded complete algebraic prequantale model. On the basis of this result, we also show that every $T_0$ topological semigroup satisfying Condition ($\Delta$) can be embedded into a compact and locally compact sober topological semigroup.