Rapor Tarihi: 13.04.2026 06:02
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Topology I | MAT309 | Turkish | Compulsory | 5. Semester | 2 + 2 | 3.0 | 6.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Doç. Dr. İzzettin DEMİR |
| Instructor(s) | |
| Goals | The objective of this course is to introduce students to the fundamental concepts of general topology and to provide a comprehensive understanding of structures such as topological spaces, bases, neighborhood systems, and accumulation points. Furthermore, by analyzing continuous functions between spaces and the concept of homeomorphism, the course aims to develop students' skills in abstract mathematical reasoning and formal proof construction. |
| Course Content | Definition and construction of topological spaces; generation of topologies via bases and subbases; neighborhood systems; adherent (closure) and accumulation (limit) points of sets; the interior, exterior, and boundary of a set; subspace topology; the concept of continuity in topological spaces and properties of continuous functions; open functions, closed functions, and the concept of homeomorphism representing the structural equivalence between two spaces. |
| # | Öğrenme Kazanımı |
| 1 | Define the concepts of topological spaces, bases, and subbases. |
| 2 | Calculate the neighborhood, adherent, accumulation, interior, exterior, and boundary points of a set. |
| 3 | Construct the subspace topology within a given topological space. |
| 4 | Analyze the continuity of functions defined on topological spaces. |
| 5 | Distinguish open and closed functions to evaluate the homeomorphism between spaces. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Topological spaces | Preparation, After Class Study, Research, Interview |
| 2. Week | Topological spaces | Preparation, After Class Study, Research, Interview |
| 3. Week | Topological spaces | Preparation, After Class Study, Research, Interview |
| 4. Week | Base and subbase | Preparation, After Class Study, Research, Interview |
| 5. Week | Base and subbase | Preparation, After Class Study, Research, Interview |
| 6. Week | The concept of neighborhood | Preparation, After Class Study, Research, Interview |
| 7. Week | The concept of neighborhood | Preparation, After Class Study, Research, Interview |
| 8. Week | Closure points | Preparation, After Class Study, Research, Interview |
| 9. Week | Closure and accumulation points | Preparation, After Class Study, Research, Interview |
| 10. Week | İnterior, exterior and boundary | Preparation, After Class Study, Research, Interview |
| 11. Week | Subspace | Preparation, After Class Study, Research, Interview |
| 12. Week | Continuity | Preparation, After Class Study, Research, Interview |
| 13. Week | Continuity | Preparation, After Class Study, Research, Interview |
| 14. Week | Open and Closed Functions, Homeomorphism | Preparation, After Class Study, Research, Interview |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 |
|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 |
| PY2 | 4 | 4 | 4 | 4 | 4 |
| PY3 | 4 | 4 | 4 | 4 | 4 |
| PY4 | 5 | 5 | 5 | 5 | 5 |
| PY5 | 1 | 1 | 1 | 1 | 1 |
| PY6 | 1 | 1 | 1 | 1 | 1 |
| PY7 | 3 | 3 | 3 | 3 | 3 |
| PY8 | 4 | 4 | 4 | 4 | 4 |
| PY9 | 4 | 4 | 4 | 4 | 4 |
| PY10 | 1 | 1 | 1 | 1 | 1 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Ders Dışı |
Homework | 14 | 2 | 28 |
| Research | 14 | 2 | 28 | |
| Interview | 14 | 2 | 28 | |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Final | 1 | 2 | 2 | |
| Total Workload | 144 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 6.0 | ||
