A Certain Class of Topological Properties

About thirty years ago it was considered that Topology had two aspects, according to which its practitioners could be roughly divided into two schools. These aspects would today be termed global and local, and those whose interests lay mainly in global properties of a space or configuration formed one school, while those whose chief interest lay in local properties formed the other. The causes for this division of interests were methodological: The com-binatorial method, stemming chiefly from the work of Poincaré and Veblen, yielded only global invariants such as the classical Betti numbers and duality theorems; while the set-theoretic method, starting from the strictly local notion of limit point, was particularly suited for the study of local properties. Thus a more accurate differentiation between the schools could be made according to method; for while the set-theoretic method allowed of the study of such concepts as local connectedness, the concepts of connectedness and uni-coherence, for example, were global; and soon the combinatorial method became adapted to the study of local properties.