| 1 | In analysis, learning the concepts of sets, functions, sequences, limits, and continuity. |
| 2 | Learning the concept of sequences in topological spaces. |
| 3 | Learning the concepts of limits, convergence, and limit points of sequences in topological spaces. |
| 4 | Learning the inadequacy of the concept of convergence of sequences in constructing topological structures in topological spaces. |
| 5 | Learning the concept of nets in topological spaces |
| 6 | Learning the concepts of limit, convergence, and limit point of nets in topological spaces |
| 7 | Learning the inadequacy of the concept of convergence of nets in establishing topological structures in topological spaces |
| 8 | Learning the concept of filters in topological spaces |
| 9 | learning the concepts of limit, convergence, and limit point of filters in topological spaces |
| 10 | learning to construct topological structures using the concept of filters in topological spaces |
| 11 | Learning to compare the concepts of continuity and sequential continuity |
| 12 | Learning to compare the concepts of limit and limit point of filters in topological spaces |
| 13 | Learning how the sustainable properties of these definitions and concepts in algebraic topology contribute to development |