Frink quasicontinuous posets.

In this paper, the concept of Frink quasicontinuous posets is introduced. The main results are: (1) a poset is a Frink quasicontinuous poset if and only if its normal completion is a quasicontinuous lattice; (2) a poset is precontinuous if and only if it is Frink quasicontinuous and meet precontinuous; (3) when a Frink quasicontinuous poset satisfies certain conditions, the way below relation has the interpolation property; (4) the category of quasicontinuous lattices with complete homomorphisms is a full reflective subcategory of the category of Frink quasicontinuous posets with cut-stable maps. [ABSTRACT FROM AUTHOR]