Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	On the parallel between normality and extremal disconnectedness
Publication Date:	2013-03-04
Authors:	- Javier Gutiérrez García - Jorge Picado
Abstract:	Several familiar results about normal and extremally disconnected (classical or pointfree) spaces shape the idea that the two notions are somehow dual to each other and can therefore be studied in parallel. In this paper we investigate the source of this ‘duality’ and show that each pair of parallel results can be framed by the ‘same’ proof. The key tools for this purpose are relative notions of normality, extremal disconnectedness, semicontinuity and continuity (with respect to a fixed class of complemented sublocales) that bring and extend to pointfree topology a variety of well-known classical variants of normality and upper and lower semicontinuities in a illuminating unified manner. Then all classical insertion and extension results will be unified under a single pointfree result.
Institution:	DMUC 13-04
Online version:	http://www.mat.uc.pt...prints/eng_2013.html
Download:	Not available