@UNPUBLISHED{publication1, title = "Remainders in pointfree topology", author = "{FERREIRA, Maria Jo{\~{a}}o} and {PICADO, Jorge} and {MARQUES PINTO, Sandra}", year = "2017-12-27", abstract = "Remainders of subspaces are important e.g. in the realm of compactifications. Their extension to pointfree topology faces a difficulty: sublocale lattices are more complicated than their topological counterparts. Nevertheless, the co-Heyting structure of sublocale lattices is enough to provide a counterpart to subspace remainders: the sublocale supplements. In this paper we give an account of their fundamental properties, emphasizing their similarities and differences with classical remainders, and provide several examples and applications to illustrate their scope. In particular, we study their behaviour under image and preimage maps, as well as their preservation by localic maps. We then use them to characterize nearly realcompact and nearly pseudocompact frames. In addition, we introduce and study hyper-real localic maps.", url = "http://www.mat.uc.pt/preprints/eng\_2017.html", note = "" }