Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/90477
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 | metadata.degois.publication.title: | Houston Journal of Mathematics | metadata.degois.publication.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: | https://hdl.handle.net/10316/90477 | Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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