| Learning Outcomes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|
| Define the concept of a metric space, provide examples of different metrics, and compare standard metrics on R^n. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the concept of subspaces in metric spaces and analyze the metric structure of a given subspace. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define Lipschitz equivalent metrics and provide examples of metrics on function spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define open and closed sets, open balls, and bounded sets, and explain the relationships among these concepts. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the concept of continuity in metric spaces (pointwise and global) and analyze isometries. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define the interior, exterior, closure, and boundary of a set and apply these concepts to examples. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain sequences and convergence in metric spaces and determine limit points. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define Cauchy sequences and explain the concept of completeness. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compare pointwise and uniform convergence and explain them through examples. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain sequential compactness and uniform continuity, and apply the Bolzano–Weierstrass theorem. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain properties of continuous functions on compact spaces and apply the Extreme Value Theorem. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the Contraction Mapping Theorem and perform basic applications. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define the concept of a topological space and explain its relationship with metric spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compare metric topologies and topologically equivalent metrics and analyze their properties. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |