| ÖÇ1 | learns the concepts of topological equivalence, surfaces, orientation, connectivity, and topological constants |
| ÖÇ2 | learns Euler's theorem on polyhedra and the concept of map coloring |
| ÖÇ3 | learns the concepts of functions, equivalence relations, continuity in the Euclidean plane, and n-dimensional Euclidean space |
| ÖÇ4 | learns about metric spaces, open and closed sets in metric spaces, and continuity in metric spaces |
| ÖÇ5 | learns about topological spaces and different methods of defining a topological space |
| ÖÇ6 | learns about bases, identification topology-quotient space, and relative topology |
| ÖÇ7 | learns about topological products and topological groups |
| ÖÇ8 | learns the concepts of Hausdorff space and normal space |
| ÖÇ9 | learns the concepts of convergence, filters, and limits |
| ÖÇ10 | learns the concepts of connected spaces and compact spaces |
| ÖÇ11 | learns the ability to understand information and skills and to interpret what they understand |
| ÖÇ12 | learns the sustainable properties of these definitions and concepts |