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A book on Topology needs no introduction. It is modern mathematics which has recently been introduced in the syllabi of Post-graduate and Honours co .... Read More
A book on Topology needs no introduction. It is modern mathematics which has recently been introduced in the syllabi of Post-graduate and Honours courses in Indian Universities. The subject based on Set Theory has gained importance in modern times. The concept of Topology being recent in mathematical world, great care has been taken to explain each detail in such a lucid style that even a High School student, having, of course, a mathematical mind, should have least difficulty in grasping bases of the subject. In order to further make it easy the subject has been tried to be brought home to student by giving a good number of solved examples in the beginning of each chapter and also unsolved examples at the end with a little hint wherever questions have been considered a bit diffcult. It is earnestly hoped that the book, the only of its kind, will be found immensely useful to teachers and students alike, studying the subject at higher level.
| Sr | Chapter Name | No Of Page |
|---|---|---|
| 1 | 0. SYMBOLS AND THEIR MEANINGS | 2 |
| 2 | 1. BASIC CONCEPTS OF SETS | 4 |
| 3 | 2. BASIC SET OPERATIONS | 8 |
| 4 | 3. RELATIONS | 6 |
| 5 | 4. FUNCTIONS | 8 |
| 6 | 5. COUNTABILITY AND SEQUENCES | 17 |
| 7 | 6. ORDERED SETS | 12 |
| 8 | 7. BOUNDED, DERIVED, OPEN AND CLOSED SETS ON THE REAL LINE | 12 |
| 9 | 8. METRIC SPACES | 58 |
| 10 | 9. TOPOLOGICAL SPACES | 70 |
| 11 | 10. BASES, SUB-BASES AND COUNTABILITY | 22 |
| 12 | 11. CONTINUOUS FUNCTIONS | 49 |
| 13 | 12. SEPARATION AXIOMS | 42 |
| 14 | 13. COMPACTNESS | 48 |
| 15 | 14. COMPLETENESS OF A METRIC SPACE | 18 |
| 16 | 15. CONNECTEDNESS | 35 |
| 17 | 16. PRODUCT SPACES | 37 |
| 18 | 17. METRIZATION | 10 |
| 19 | 18. NETS AND CONVERGENCE | 15 |
| 20 | 19. FILTERS AND ULTRAFILTERS | 21 |
| 21 | 20. PARACOMPACT SPACES | 3 |
| 22 | 21. HOMOTOPY AND FUNDAMENTAL GROUP | 3 |
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