Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/89466
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. | URI: | https://hdl.handle.net/10316/89466 | DOI: | 10.36045/bbms/1382448188 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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