Abstract
As a common generalization of s2-quasicontinuous posets and quasi Z-continuous domains, the concept of sZ-quasicontinuous posets is introduced and some of their basic properties are investigated. It is proved that if a subset system Z satisfies certain conditions, and P is an sZ-quasicontinuous poset, then the Z-way below relation ≪Z on P has the interpolation property, the space (P,σZ(P)) is locally compact and the space (P,λZ(P)) is a pospace. It is also proved that under some conditions, a poset is sZ-continuous if and only if it is meet sZ-continuous and sZ-quasicontinuous.
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