<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Some aspects of (non)functoriality of natural discrete covers of locales |
Publication Date: | 2018-03-26 |
Authors: |
- Richard N. Ball
- Jorge Picado - Ales Pultr |
Abstract: | The frame Sc(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 Sc(L) are isomorphic. The construction Sc is not functorial; this leads to the question of individual liftings of homomorphisms L→ M to homomorphisms Sc(L)→Sc(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 Sc(L) are naturally isomorphic), and finally present liftings of h:L→ M for regular L and arbitrary Boolean M. |
Institution: | DMUC 18-10 |
Online version: | http://www.mat.uc.pt...prints/eng_2018.html |
Download: | Not available |