Back to Search
Start Over
Some aspects of (non) functoriality of natural discrete covers of locales.
- Source :
-
QM - Quaestiones Mathematicae . Aug2019, Vol. 42 Issue 6, p701-715. 15p. - Publication Year :
- 2019
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONSTRUCTION
Subjects
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 42
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 137924167
- Full Text :
- https://doi.org/10.2989/16073606.2018.1485756