| Learning Outcomes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|
| Define the concept of subspaces in topological spaces and analyze subspace examples in R^n. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the concept of continuity in topological spaces and apply fundamental continuity theorems. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the concepts of bases and subbases of a topology and define second countable spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define the product topology and explain the basic properties of product spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Apply the concepts of interior, exterior, closure, and boundary of a set in topological spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define separation axioms (T0, T1, Hausdorff) and classify spaces accordingly. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the concept of homeomorphism and analyze topologically equivalent spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Distinguish between topological properties and hereditary properties and explain them with examples. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define quotient spaces and apply them to fundamental examples. | - | - | - | - | - | - | - | - | - | - | - |
| Explain the concepts of connectedness, connected components, and path-connectedness. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Topolojik uzaylarda kompaktlık kavramını tanımlar ve özelliklerini analiz eder. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the Heine–Borel Theorem and perform its applications. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compare and evaluate the relationships between compactness and sequential compactness. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Formulate and solve mathematical problems involving abstract topological structures. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |