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Title: Joins of closed sublocales
Authors: Picado, Jorge 
Pultr, Aleš 
Tozzi, Anna 
Keywords: Frame, locale, sublocale, nucleus, sublocale lattice, coframe, open sublocale, closed sublocale, T1-space, induced subspace, subfit frame, fit frame, Booleanization.
Issue Date: 2019
Publisher: University of Houston
Project: UID/MAT/00324/2013 
Serial title, monograph or event: Houston Journal of Mathematics
Volume: 45
Abstract: Sublocales that are joins of closed ones constitute a frame S_Vc(L) embedded as a sup-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 T_1-space X, S_Vc(\Omega(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 of S(L).
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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