Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/90473
Title: | Some aspects of (non) functoriality of natural discrete covers of locales | Authors: | Ball, Richard N. Picado, Jorge Pultr, Aleš |
Keywords: | Frame, locale, sublocale, sublocale lattice, essential extension, subfit, Booleanization | Issue Date: | 2019 | Publisher: | Taylor & Francis | Project: | UID/MAT/00324/2013 | Serial title, monograph or event: | Quaestiones Mathematicae | Volume: | 42 | Issue: | 6 | Abstract: | The frame S_c(L) generated by closed sublocales of a locale L is known to be a natural Boolean (“discrete”) extension of a subfit L; also it is known to be its maximal essential extension. In this paper we first show that it is an essential extension of any L and that the maximal essential extensions of L and S_c(L) are isomorphic. The construction S_c is not functorial; this leads to the question of individual liftings of homomorphisms L → M to homomorphisms S_c(L) → S_c(M). This is trivial for Boolean L and easy for a wide class of spatial L, M. Then, we show that one can lift all h : L → 2 for weakly Hausdorff L (and hence the spectra of L and S_c(L) are naturally isomorphic), and finally present liftings of h : L → M for regular L and arbitrary Boolean M. | URI: | https://hdl.handle.net/10316/90473 | DOI: | 10.2989/16073606.2018.1485756 | Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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BallPicadoPultrQM.pdf | 228.42 kB | Adobe PDF | View/Open |
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