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Title: Perfect locales and localic real functions
Authors: Gutiérrez García, Javier
Kubiak, Tomasz
Picado, Jorge 
Keywords: Locale, Sublocale, Perfectness, G_\delta-perfectness, Perfect normality, Semicontinuous real function, Insertion theorem.
Issue Date: 2020
Publisher: Springer
Project: UID/MAT/00324/2019 
Serial title, monograph or event: Algebra Universalis
Volume: 81
Issue: 32
Abstract: 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.
DOI: 10.1007/s00012-020-00661-x
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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