Hewitt's irresolvability and induced sublocales in spatial frames (Preprint)

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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
 
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