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|Title:||Joins of closed sublocales||Authors:||Picado, Jorge
|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).||URI:||http://hdl.handle.net/10316/90477||Rights:||embargoedAccess|
|Appears in Collections:||I&D CMUC - Artigos em Revistas Internacionais|
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