Perfect locales and localic real functions

The purpose of this paper is to identify the role of perfectness in the Michael insertion theorem for perfectly normal locales. We attain it by characterizing perfect locales in terms of strict insertion of two comparable lower semicontinuous and upper semicontinuous localic real functions. That cha...

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Detalles Bibliográficos
Autores: Gutiérrez García, Francisco Javier, Kubiak, Tomasz, Picado, Jorge
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/70647
Acceso en línea:http://hdl.handle.net/10810/70647
Access Level:acceso abierto
Palabra clave:locale
sublocale
perfectness
G -perfectness
perfect normality
semicontinuous real function
insertion theorem
Descripción
Sumario:The purpose of this paper is to identify the role of perfectness in the Michael insertion theorem for perfectly normal locales. We attain it by characterizing perfect locales in terms of strict insertion of two comparable lower semicontinuous and upper semicontinuous localic real functions. That characterization, when combined with the insertion theorem for normal locales, provides an improved formulation of the aforementioned pointfree form of Michael's insertion theorem.