Universal Bounds and Monotonicity of Ordinal Invariants

Abstract

Abstract. The tightness of a topological space provides a universal bound for all ordinal invariants determined by weak topologies generated by collections of subsets. It is the purpose of this paper to present the following very inclusive results. The cardinal successor of the tightness of a topological space, t(X)+, provides the universal bound for all ordinal invariants determined by any weak topology on X generated by a collection of subsets. Also, all ordinal invariants are monontonic decreasing for pseudo-open mappings.