MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT6004 | Advanced Topology II | Spring | 3 | 0 | 3 | 8 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | Turkish |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ATABEY KAYGUN |
Recommended Optional Program Components: | None |
Course Objectives: | The aim of the courses is to provide developing of “General Topology” courses as in graduate level. |
The students who have succeeded in this course; 1 Be able to understand the importance of mathematics and especially some extensions in topology 2 To improve the ability to get results by arguments to find the solutions of the problems 3 Be able to comment events in a different point of view 4 Be able to improve mathematical sense. |
Baire’s Category Theorem, Completeness and compactness, Function spaces, Point open topology, Compact open topology, Ascoli’s theorem, The concepts of locally finite, Paracompactness, Lightly compact spaces and duality. |
Week | Subject | Related Preparation |
1) | Complete spaces | |
2) | Baire’s Category Theorem. Completeness and compactness | |
3) | Completeness and compactness | |
4) | contraction transformations | |
5) | Completeness and Baire spaces | |
6) | Function spaces | |
7) | Point open topology | |
8) | Toplogy of Uniform continuity | |
9) | Ascoli theorem | |
10) | Uniform spaces | |
11) | Uniform spaces | |
12) | Local finiteness, paracompactness | |
13) | Local finiteness, paracompactness | |
14) | Lightly compakt spaces and its duals |
Course Notes / Textbooks: | Prof. Dr. Gulhan ASLIM, “ Genel Topoloji”, Ege Uni. Fen Fakultesi Yayinlari, (1998) Lipschutz, S., “ General Topology”, Schaum. Pub. Co. New york, (1964). Munkres, J. P., “ Topology a First Course”, Prentice Hall. Inc., (1975). Willard, S. “General Topology”, Addision-Wesley Publishing Company, 1970. Engelking, R. "General Topology" Heldermann Verlag, Berlin 1989. |
References: |
Semester Requirements | Number of Activities | Level of Contribution |
Presentation | 1 | % 20 |
Midterms | 1 | % 30 |
Final | 1 | % 50 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 6 | 84 |
Presentations / Seminar | 1 | 30 | 30 |
Midterms | 1 | 22 | 22 |
Final | 1 | 22 | 22 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |