General Topology Pdf

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This course will have two goals: To introduce examples of topological spaces, illustrating various phenomena, and conveying something of topology's geometric flavour. To develop the foundations of topology relied upon in higher courses.

Chapter 2. Topological Spaces and Continuous Functions. Section 12. Topological Spaces. PDF. Section 13. Basis for a Topology. PDF. Supplement. Proofs of Theorems in Section 13. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 13. PDF. Section 14. The Order Topology. PDF. Supplement. Proofs of Theorems in Section 14. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 14. PDF. Section 15. The Product Topology on X × Y. PDF. Supplement. Proofs of Theorems in Section 15. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 15. PDF. Section 16. The Subspace Topology. PDF. Supplement. Proofs of Theorems in Section 16. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 16. PDF. Section 17. Closed Sets and Limit Points. PDF. Supplement. Proofs of Theorems in Section 17. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 17. PDF. Section 18. Continuous Functions. PDF. Supplement. Proofs of Theorems in Section 18. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 18. PDF. Section 19. The Product Topology. PDF. Supplement. Proofs of Theorems in Section 19. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 19. PDF. Section 20. The Metric Topology. PDF. Supplement. Proofs of Theorems in Section 20. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 20. PDF. Section 21. The Metric Topology (continued). PDF. Supplement. Proofs of Theorems in Section 21. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 21. PDF. Section 22. The Quotient Topology. PDF. Supplement. Proofs of Theorems in Section 22. PDF (prepared in Beamer). Supplement. Printout of the Proofs of Theorems in Section 22. PDF. Section 22S. Supplement: Topological Groups. PDF. (This section includes definitions of the general linear group, the special linear group, the orthogonal group, and the special orthogonal group, each over the reals.) Study Guide 2.

The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.

Applications of metrics include error-correcting codes and social choice. Pseudometrics, quasi-metrics, and partial metrics are explored. Connections between topology and order are examined. Over 740 exercises, from standard to novel, are included. 2b1af7f3a8