Duality theory for the category of stable compactifications - Bezhanishvili, G.; Harding, J. (Topology Proceedings, 2021)
We introduce the category of stable compactifications of T_0-spaces and obtain a dual description of it in terms of what we call Raney extensions of proximity frames. These are proximity frame embeddings of a regular proximity frame into a Raney lattice, i.e. the lattice of upsets of a poset. This duality generalizes the duality between compactifications of completely regular spaces involving de Vries extensions given in [8]. It also specializes to give a duality between T_0-spaces and Raney extensions that are maximal in a certain sense. This duality is related to the duality for T_0-spaces given in [7] using the notion of a Raney algebra, i.e. a Raney lattice with a certain type of interior operator.