Z-abstract Basis

In this paper, the notion of a Z-abstract basis is defined and its properties are discussed. It is proved that for a union-complete subset system, the basis of a Z-continuous poset, with the restricted ≪Z-relation, is a Z-abstract basis and the rounded Z-ideal completion of the Z-abstract basis is isomorphic to the Z-continuous poset. Conversely, the rounded Z-ideal completion of a Z-abstract basis is a Z-continuous poset.