Sentences Preserved between Equivalent Topological Bases

A syntactical characterization will be proved, with respect to a suitable language for topology, of those sentences whose truth in one base of a topological space implies their truth in all bases of the space. Or, restating this, those sentences whose truth for a space can be ‘equivalently tested in any base for the space. (An example is the HAUSDORFF axiom -that every two points are separated by open sets is equivalent to every two points being separated by basic sets.) The author wishes to express gratitude to Professor H. JEROME KEISLER, his most helpful and patient thesis advisor.