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october 2013 Insertion and extension results for pointfree complete regularity
Javier Gutiérrez García, Jorge Picado
Bull. Belg. Math. Soc. Simon Stevin 20(4): 675-687 (october 2013). DOI: 10.36045/bbms/1382448188


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 weaker class of frames introduced in this paper (called \emph{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.


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Javier Gutiérrez García. Jorge Picado. "Insertion and extension results for pointfree complete regularity." Bull. Belg. Math. Soc. Simon Stevin 20 (4) 675 - 687, october 2013.


Published: october 2013
First available in Project Euclid: 22 October 2013

zbMATH: 1284.06020
MathSciNet: MR3129067
Digital Object Identifier: 10.36045/bbms/1382448188

Primary: 06D22
Secondary: ‎54C30 , 54D15

Keywords: $C$-embedding , $C^*$-embedding , compact sublocale , compact-like real function , complete regular frame , completely separated sublocales , frame , insertion , insertion theorem , locale , lower semicontinuous , Sublocale , upper semicontinuous

Rights: Copyright © 2013 The Belgian Mathematical Society


Vol.20 • No. 4 • october 2013
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