A theory of quantale-enriched dcpos and their topologization
There have been developed several approaches to a quantale-valued quantitative domain theory. If the quantale Q is integral and commutative, then Q-valued domains are Q-enriched, and every Q-enriched domain is sober in its Scott Q-valued topology, where the topological «intersection axiom» is expres...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/58322 |
| Acceso en línea: | http://hdl.handle.net/10810/58322 |
| Access Level: | acceso abierto |
| Palabra clave: | unital quantale subdistributive quasi-magma on a quantale ⋄-flat contravariant |
| Sumario: | There have been developed several approaches to a quantale-valued quantitative domain theory. If the quantale Q is integral and commutative, then Q-valued domains are Q-enriched, and every Q-enriched domain is sober in its Scott Q-valued topology, where the topological «intersection axiom» is expressed in terms of the binary meet of Q (cf. D. Zhang, G. Zhang, Fuzzy Sets and Systems (2022)). In this paper, we provide a framework for the development of Q-enriched dcpos and Q-enriched domains in the general setting of unital quantales (not necessarily commutative or integral). This is achieved by introducing and applying right subdistributive quasi-magmas on Q in the sense of the category Cat(Q). It is important to point out that our quasi-magmas on Q are in tune with the «intersection axiom» of Q-enriched topologies. When Q is involutive, each Q-enriched domain becomes sober in its Q-enriched Scott topology. This paper also offers a perspective to apply Q-enriched dcpos to quantale computation |
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