Sheldon Davis' text is written for introductory courses in topology taken by advanced undergraduate and beginning graduate students. Designed to be flexible, the text is divided into two parts to accomodate different courses, course configurations, and instructor preferences. Part I of the text covers the bare essentials every student should know about topology before continuing on to study point-set or set-theoretic topology, algebraic topology, funcitonal analysis, continuum theory, or the many other important areas in mathematics that utilize topology fundamentals. To keep the text manageable for beginning students, use of set theory in Part I is kept to an intuitive level. Part II contains a complete beginning course in general topology, or set-theoretic topology. General topology courses that assume prior background in the fundamentals can start directly with Part II and use the material in Part I for conceptual review. This text is part of the Walter Rudin Student Series in Advanced Mathematics. 

Part I 1 Sets, Functions, Notation 2 Metric Spaces 3 Continuity 4 Topological Spaces 5 Basic Constructions: New Spaces From Old 6 Separation Axioms 7 Compact Spaces 8 Locally Compact Spaces 9 Connected Spaces 10 Other Types of Connectivity 11 Continua 12 Homotopy Part II 13 A Little More Set Theory 14 Topological Spaces II 15 Quotients and Products 16 Convergence 17 Separation Axioms II 18 Compactness and Countability Properties 19 Stone-Cech Compactification 20 Paracompact Spaces 21 Metrization

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