Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Joins of closed sublocales
Publication Date:	2016-08-22
Authors:	- Jorge Picado - Ales Pultr - Anna Tozzi
Abstract:	Sublocales that are joins of closed ones constitute a frame S_Vc(L) embedded as a join-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L). In case of a T₁-space X, S_Vc(Ω(X)) picks precisely the sublocales corresponding to induced subspaces. In linear L and more generally if L is also a coframe, S_Vc(L) is both a frame and a coframe, but with trivial exceptions not Boolean and not a subcolocale.
Institution:	DMUC 16-39
Online version:	http://www.mat.uc.pt...prints/eng_2016.html
Download:	Not available