A note on regular and completely regular topological spaces
Michael J. Norris · Proceedings of the American Mathematical Society · 1950
michael j. norrisFor the purposes of this note we shall consider a topological space to be a F-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.In-