More sum theorems for topological spaces

Abstract

By a sum theorem for topological spaces is meant a theorem of the following type: If ^~ is a cover of a space X, each element of which possesses a property ^*, then X also possesses the property &*. Different types of sum theorems for various classes of topological spaces have been obtained from time to time by various authors. Perhaps the simplest known sum theorem is the locally finite sum theorem which states the following: If {F a : a] be a locally finite closed covering of a space X such that each F a possesses a property ^*, then X possesses The locally finite sum theorem is shown to hold for a large number of important topological properties.