General Topology
Dr. N.K. Aggarwal, "General Topology"
English | ASIN B0BL9BCDC4 | 2022 | 268 pages | PDF | 69 MB
English | ASIN B0BL9BCDC4 | 2022 | 268 pages | PDF | 69 MB
CONTENTS
Units Page No.
1. Topological Spaces 1
2. Basis for Topology 29
3. The Order Topology 36
4. The Product Topology on X × Y 41
5. The Subspace Topology 54
6. Closed Sets and Limit Point 62
7. Continuous Functions 68
8. The Product Topology 78
9. The Metric Topology 84
10. The Quotient Topology 100
11. Connected Spaces, Connected Subspaces of Real Line 106
12. Components and Local Connectedness 116
13. Compact Spaces and Compact Subspace of Real Line 124
14. Limit Point Compactness 133
15. Local Compactness 138
16. The Countability Axioms 143
17. The Separation Axioms 153
18. Normal Spaces, Regular Spaces and Completely Regular Spaces 164
19. The Urysohn Lemma 173
20. Urysohn Metrization Theorem 180
21. The Tietze Extension Theorem 186
22. The Tychonoff Theorem 190
23. The Stone-Cech Compactification 196
24. Local Finiteness and Paracompactness 202
25. The Nagata-Smirnov Metrization Theorem 211
26. The Smirnov Metrization Theorem 216
27. Complete Metric Spaces 219
28. Compactness in Metric Spaces 228
29. Pointwise and Compact Convergence 228
30. Ascoli’s Theorem 246
31. Baire Spaces 251
32. Introduction to Dimension Theory 257