MAT6003 Advanced Topology IBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
PhD. TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6003 Advanced Topology I Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

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” as graduate level.

Learning Outcomes

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

Course Content

Convergens, nets, filters, subnets, ultra filters in topological spaces, Tychonoff theorem, Locally compact spaces, Compactification, Compactness in metric space, Components, Completely disconnected spaces, arcwise connected spaces.

Weekly Detailed Course Contents

Week Subject Related Preparation
2) Convergens in topological spaces
3) Nets in topological spaces
4) Nets in topological spaces
5) Filters in topological spaces
6) Filters in topological spaces
7) Subnets, ultra filters in topological spaces
8) Subnets, ultra filters in topological spaces
9) Tychonoff theorem
10) Tychonoff theorem
11) Locally compact spaces
12) Compactification
13) Compactness in metric space
14) Completely disconnected spaces, arcwise connected spaces


Course Notes / Textbooks: )Prof. Dr. Gülhan ASLIM, “ Genel Topoloji”, Ege Üni. Fen Fakültesi Yayınları, (1998) 2)Munkres, J. P., “ Topology a First Course”, Prentice Hall. Inc., (1975). 3)Kuratowski, C., “ Topologie I.", Wydawnictwo naukewe Warsawa, (1958). 4)Kelley, John. L., “General Topology”, Springer-Verlag , (1955). 5)Willard, S. “General Topology”, Addision-Wesley Publishing Company, 1970 6)Engelking,R.,"General Topology",Heldermann Verlag Berlin,1989.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Presentation 1 % 20
Midterms 1 % 30
Final 1 % 50
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 5 70
Presentations / Seminar 1 20 20
Midterms 1 33 33
Final 1 35 35
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution