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   Preface I. BASIC TOPICS.  1. Open and Closed Subsets.  2. Building Open and Closed Subsets.  3. Continuity.  4. Homeomorphism.  5. Cantor Sets and Allied Topics.  6. Embeddings.  7. Connectivity .  8. Path Connectedness.  9. Closure and Limit Points. 10. Compactness. 11. Local Connectivity. II. ADVANCED TOPICS 12. Space Filling Curves. 13. Manifolds. 14. Knots and Kottings. 15. Simple Connectivity. 16. Deformation Type. 17. Complexes. 18. Higher Dimensions. 19. The Poincare Conjecture. III. APPENDICES. Appendix A. Sets and Logic. Appendix B. Numbers. Appendix C. Cardinality of Sets. Appendix D. Summary from Calculus. Appendix E. Strategy in Proof. Bibliography. Index of Examples, Remarks, and Propositions. Subject Index.

Offering an introduction to topics of topology, this book is designed both for students who take only one course in topology and for those who are preparing for advanced work. It provides concrete examples, and guidance for building reasoning skills and writing proofs.

Elementary topology