Abstract
For the purposes of this note we shall consider a topological space to be a T-space; that is, the family of open sets for the space is closed under finite intersection and arbitrary union and contains both the void set and the space itself. We shall be interested in classes of topological spaces having the same points; this common set of points we call the basic point set for the spaces. It is well known that the class of topological spaces S for a given basic point set can be partially ordered by means of the inclusion relation for the families of open sets. One such topological space is said to be greater than another if the family of open sets for the former includes the family of open sets for the latter. With reference to this order relation, S is a complete lattice. Indeed, if {SxIXCM is a subset of S and VO is the family of open sets for SA, then IElxA VX is the family of open sets for the greatest lower bound of { SA I X CA }, and the family V of open sets for the least upper bound of this subset is given by:
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