## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Insertion and extension results for pointfree complete regularity

#### 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 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 4 (2013), 675-687.

Dates
First available in Project Euclid: 22 October 2013

https://projecteuclid.org/euclid.bbms/1382448188

Digital Object Identifier
doi:10.36045/bbms/1382448188

Mathematical Reviews number (MathSciNet)
MR3129067

Zentralblatt MATH identifier
1284.06020

#### Citation

Gutiérrez García, Javier; Picado, Jorge. Insertion and extension results for pointfree complete regularity. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 4, 675--687. doi:10.36045/bbms/1382448188. https://projecteuclid.org/euclid.bbms/1382448188