Language: English
Pages: 70
1.2. Functions......Page 3
1.5. Relations......Page 4
2. The integers and the real numbers......Page 7
3. Products and coproducts......Page 9
4. Finite and infinite sets......Page 10
5. Countable and uncountable sets......Page 12
6. Well-ordered sets......Page 14
7. Partially ordered sets, The Maximum Principle and Zorn's lemma......Page 16
8.4. Subbasis and basis for a topology......Page 18
10. The product topology......Page 20
11. The subspace topology......Page 21
11.5. Subspaces of linearly ordered spaces......Page 22
12.3. Closure and interior......Page 24
12.10. Limit points and isolated points......Page 25
12.14. Convergence, the Hausdorff property, and the T1-axiom......Page 26
13. Continuous functions......Page 27
13.6. Homeomorphisms and embeddings......Page 28
13.13. Maps into products......Page 29
13.17. Maps out of coproducts......Page 30
14.2. Quotient topologies and quotient maps......Page 31
15.6. The first countability axiom......Page 37
15.13. The uniform metric......Page 39
16. Connected spaces......Page 40
17. Connected subsets of linearly ordered spaces......Page 42
17.9. Components and path components......Page 43
17.12. Locally connected and locally path connected spaces......Page 44
18. Compact spaces......Page 47
19. Compact subspaces of linearly ordered spaces......Page 50
19.6. Compactness in metric spaces......Page 51
21. Locally compact spaces and the Alexandroff compactification......Page 53
22. Countability axioms......Page 57
23. Separation Axioms......Page 58
24. Normal spaces......Page 60
25.1. An embedding theorem......Page 62
25.5. A universal second countable regular space......Page 63
26.6. The Stone--Cech construction......Page 65
27. Manifolds......Page 68
28. Relations between topological spaces......Page 69
References......Page 70
