@UNPUBLISHED{publication1, title = "Axiom T\_D and the Simmons sublocale theorem", author = "{PICADO, Jorge} and {PULTR, Ales}", year = "2018-11-18", abstract = " More precisely, we are analyzing some of Simmons, Niefield and Rosenthal results concerning sublocales induced by subspaces. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom TD for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. Niefield and Rosenthal avoided discussing this condition altogether. In this paper we show that the role of TD in this question is crucial. Concentration on the properties of TD-spaces and technique of sublocales in this context allows us to present a simple, transparent and choice-free proof of the scatteredness theorem. ", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }