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...

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Detalles Bibliográficos
Autores: Gutiérrez García, Francisco Javier, Höhle, Ulrich
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
Descripción
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.