Recently, Rusu and Ciobanu established that for a continuous domain L, a subset B of L is a basis if and only if B is dense with respect to the d-topology, called the density topology, on L. In situations where directed completeness fails, Erné has proposed in 1991 an alternative definition of continuity called s
2-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 of s
2-continuous posets with appropriate modifications. Although we obtain more properties of essential topologies and density topologies on s
2-continuous posets, respectively.