Essential and density topologies ons2-continuous posets

Abstract

Recently, Rusu and Ciobanu established that for a continuous domainL, a subsetBofLis a basis if and only ifBis dense with respect to thed-topology, called the density topology, onL. In situations where directed completeness fails, Erné has proposed in 1991 an alternative definition of continuity calleds2-continuity which remedied the lack of stability of continuity under the classical Dedekind–MacNeille completion. In this paper, we show how the ‘Rusu–Ciobanu’ type of characterization can be formulated and established over the class ofs2-continuous posets with appropriate modifications. Although we obtain more properties of essential topologies and density topologies ons2-continuous posets, respectively.