Continuous prequantale models of \(T_1\) topological semigroups. (English) Zbl 07513475
Jung, Achim (ed.) et al., Proceedings of the 8th international symposium on domain theory and its applications, ISDT 2019, Yangzhou, China, June 14–17, 2019. Amsterdam: Elsevier. Electron. Notes Theor. Comput. Sci. 345, 99-111 (2019).
Summary: In this paper, we show that every \(T_1\) topological semigroup satisfying condition \((\Delta)\) can be embedded into a topological semigroup \((D, \sigma, \odot)\), where \((D, \sqsubseteq)\) is a domain. Furthermore, by considering the maximal point topological semigroup of a continuous prequantale, it is proven that every \(T_1\) topological semigroup satisfying condition \((\Delta)\) has a continuous prequantale model, which may not be bounded complete.
For the entire collection see [Zbl 1420.68011].
For the entire collection see [Zbl 1420.68011].
MSC:
68Q55 | Semantics in the theory of computing |
06B35 | Continuous lattices and posets, applications |
06F07 | Quantales |
22A25 | Representations of general topological groups and semigroups |
Keywords:
topological semigroup; prequantale; stable ordered semigroup; Scott topology; prequantale modelReferences:
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