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.
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.
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