Formal methods based on the mathematical theory of partially ordered sets (i.e., posets) have been used for the description of topological relations among spatial objects since many years. In particular, the use of the lattice completion (or normal completion) of a poset modeling a set of spatial objects has been shown by Kainz, Egenhofer and Greasley to be a fundamental technique to build meaningful representations for topological relations. In a companion paper [3] we have discussed the expressive power of the lattice completion as a formal model for a set of spatial objects. In this paper we prove sufficient and necessary conditions for its use to give a correct representation of intersection and union relations among spatial objects. We also show how to use lattice completion when working on a subset (i.e., a view) of the set of spatial objects so that the computation only considers objects relevant to the view itself.