Topological Groups
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Topological Groups | MAT528 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Halis AYGÜN
Prof. Dr. Çiğdem GÜNDÜZ
Associate Prof. Dr. Vildan ÇETKİN
Associate Prof. Dr. Banu PAZAR VAROL
Learning Outcomes of the Course Unit
1) Explain the concept of a topological group.
2) Explain the concept of a neighborhood structure of a point in a topological group and some of its properties.
3) State the fundamental properties of connectedness, completeness and compactness of a topological group.
4) Explain the topological group homomorphisms.
5) State the concept of a topological transformation group and some of its basic properties.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Topology I, Algebra I
Course Contents
This course provides candidates with in-depth knowledge on group, definitions of topology and topological group, neigborhood system and its properties of a point in a topological group, morphisms in a topological group, subgroups, quotient groups, product spaces and topological groups, direct product of topological groups, connected and totally disconnected topological groups, uniform structures on a topological group, complete groups, the concepts of compactness and local compactness in topological groups, topological transformation groups.
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
1) Question-Answer
2) Discussion
3) Drill and Practice
4) Self Study
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required