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Title: Insertion and extension results for pointfree complete regularity
Authors: Gutiérrez García, Javier
Picado, Jorge 
Keywords: Frame, locale, sublocale, completely separated sublocales, compact sublocale, compact-like real function, complete regular frame, upper semicontinuous, lower semicontinuous, insertion, insertion theorem, C-embedding, C∗-embedding
Issue Date: 2013
Project: PEst-C/MAT/UI0324/2013 
Serial title, monograph or event: Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume: 20
Issue: 4
Abstract: There are insertion-type characterizations in pointfree topology that extend well known insertion theorems in point-set topology for all relevant higher separation axioms with one notable exception: complete regularity. In this paper we fill this gap. The situation reveals to be an interesting and peculiar one: contrarily to what happens with all the other higher separation axioms, the extension to the pointfree setting of the classical insertion result for completely regular spaces characterizes a formally weakerclass of frames introduced in this paper (called completely c-regular frames). The fact that any compact sublocale (quotient) of a completely regular frame is a C-sublocale (C-quotient) is obtained as a corollary.
DOI: 10.36045/bbms/1382448188
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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