PRINCIPLES OF TOPOLOGY

Topology is a natural geometric and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis.Customary topics of point-set topology include metric spaces general topological spaces continuity topological equivalence basis subbasis connectedness compactness separation properties metrization subspaces product spaces and quotient spaces. In addition the text introduces geometric differential and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.