Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: continuous topology, represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and geometric topology, covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340 exercises in all). The text's value as a reference work is enhanced by a collection of historical notes, a bibliography, and index. 1970 edition. 27 figures.