1 | Metric spaces. |
2 | Open, closed sets, and continuity iin metric spaces. |
3 | Topological spaces. basis, subbasis, subspaces. |
4 | Neighborhood ,Limit, interior and boundary points. The notion of convergence. |
5 | Continuous functions and homeomorphism. |
6 | Construction of topological spaces: subspaces, product, and quotient spaces. |
7 | Countability axioms,Lindelof, first and second countable spaces. |
8 | Seperable spaces. Separation axioms. |
9 | T_0 , T_1 and Hausdorff spaces.Midterm Exam. |
10 | Regular and normal spaces. |
11 | Urysohn s and Tietze s theorems. |
12 | Compactness, sequential compactness, compactification, separation axioms. |
13 | Connectedness,connected components,path conncetednes, path components. |
14 | Topological groups. |