Enriched topologies and topological representation of semi-unital quantales
This paper presents the topologization of semi-unital and semi-integral quantales by means of enriched topologies. In a first step we show that semi-unital and semi-integral quantales can be represented by a specific type of right cQ2-algebras in Sup where cQ2 is the unitalization of the quantizatio...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/70625 |
| Acceso en línea: | http://hdl.handle.net/10810/70625 |
| Access Level: | acceso abierto |
| Palabra clave: | enriched category theory Right M-module enriched topology semi-unital quantale prime element |
| Sumario: | This paper presents the topologization of semi-unital and semi-integral quantales by means of enriched topologies. In a first step we show that semi-unital and semi-integral quantales can be represented by a specific type of right cQ2-algebras in Sup where cQ2 is the unitalization of the quantization of 2. In a second step we use this identification and construct the corresponding cQ2-enriched sober spaces. On this basis semi-unital and spatial quantales are characterized by cQ2-enriched topologies. A consequence of these constructions is a natural topologization of the quantale of all closed left (resp. right) ideals of a non-commutative and unital C -algebra. |
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