| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 4 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Know basic concepts in topological spaces.
- Classifie the topological spaces.
- Define the topology of product and quotient spaces and analyses the properties of these spaces.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | No |
|---|
| Course Description | In this course, the topics covered include the concept of topological structure and topological space, open and closed sets in topological spaces, comparison of topologies, the concept of topological subspace, the topology of real numbers, the plane, and metric spaces, topological equivalence, the concept of neighborhood, contact points, accumulation points, closure, the interior and exterior of a set, the boundary of a set, as well as product and quotient spaces. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Topology and basic concepts |
|
2nd Week |
Concept of topological space |
|
3rd Week |
Open and closed sets in topological space |
|
4th Week |
Closure of a set, dense set |
|
5th Week |
Concept of topological subspace |
|
6th Week |
Topology of real numbers, plane |
|
7th Week |
Topology of metric space |
|
8th Week |
Midterm |
|
9th Week |
Neighbourhood concept |
|
10th Week |
Accumulation point and related examples |
|
11th Week |
Continuity |
|
12th Week |
Cartesian product spaces |
|
13th Week |
Quotient spaces |
|
14th Week |
Quotient spaces |
|
15th Week |
General review |
|
| Recommended or Required Reading | Genel Topoloji; Prof.Dr.Cemil Yıldız
Genel Topoloji; Prof.Dr.Gülhan Aslım
Topology, James Munkres, Prentice Hall 2000 |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Total(%) |
|
40 |
| Contribution of In-term Studies to Overall Grade(%) |
|
40 |
| Contribution of Final Examination to Overall Grade(%) |
|
60 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
|
|
|
| Individual or group work |
13 |
4 |
52 |
| Preparation for Final exam |
1 |
15 |
15 |
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
10 |
10 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 120 |
| Total Work Load / 30 (h) | 4 |
| ECTS Credit of the Course | 4 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
