@UNPUBLISHED{publication1, title = "Hewitt's irresolvability and induced sublocales in spatial frames", author = "{BABOOLAL, Dharmanand} and {PICADO, Jorge} and {PILLAY, Paranjothi} and {PULTR, Ales}", year = "2019-02-02", 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). ", url = "http://www.mat.uc.pt/preprints/eng\_2019.html", note = "" }