MAT6004 Advanced Topology IIBahçeşehir 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
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.

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” courses as in 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

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.

Weekly Detailed Course Contents

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.

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 6 84
Presentations / Seminar 1 30 30
Midterms 1 22 22
Final 1 22 22
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