<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Hewitt's irresolvability and induced sublocales in spatial frames |
Publication Date: | 2019-02-02 |
Authors: |
- Dharmanand Baboolal
- Jorge Picado - Paranjothi Pillay - Ales Pultr |
Abstract: | Sublocales of frames, even those representing subspaces (induced sublocales), are typically not complemented in the lattice of all sublocales. We present a necessary and sufficient condition for an induced sublocale to be so, and prove that all induced sublocales are complemented if and only if the space in question is hereditarily irresolvable, a property slightly weaker than — and in a broad class of spaces equivalent with — scatteredness (under which condition, by Simmons' result all sublocales are complemented). |
Institution: | DMUC 19-05 |
Online version: | http://www.mat.uc.pt...prints/eng_2019.html |
Download: | Not available |