| 1 | Learn the concepts of topological equivalence, surfaces, orientation, connectedness, and topological constants. |
| 2 | Learn the Euler theorem on polyhedra and the concept of coloring maps. |
| 3 | Learn the concepts of functions, equivalence relations, continuity in the Euclidean plane, and n-dimensional Euclidean space. |
| 4 | Learn the concepts of metric spaces and continuity in metric spaces. |
| 5 | Learn the concepts of open and closed sets in metric spaces. |
| 6 | Learn the concepts of topological spaces and different methods of defining a topological space. |
| 7 | Learn the concepts of bases and relative topology. |
| 8 | Learn the concepts of identification topology and quotient spaces. |
| 9 | learning the concept of topological product |
| 10 | learning the concepts of topological groups and compact spaces |
| 11 | learning the concepts of Hausdorff spaces and normal spaces |
| 12 | learning the concepts of convergence and filters |
| 13 | learning the concepts of limits and connected spaces |
| 14 | learning the sustainable properties of these definitions and concepts |