MATH420 POINT-SET TOPOLOGY
| Course Code: | 2360420 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will learn:
- the fundamental concepts of point-set topology
- the notions of compactness and connectedness
- the countability and separation axioms
- the quotient topology with its properties
Course Content
Topological Spaces; basis, subbasis, subspaces. Closed sets, limit points. Hausdorff Spaces. Continuous functions, homeomorphisms. Product topology. Connected spaces, compo-nents, path connectedness, path components. Compactness, sequential compactness, compactness in metric spaces. Definition of regular and normal spaces. Urysohn`s Lemma, Tietsze Extension Theorem.
Course Learning Outcomes
The students who succeed in this course;
- will be able to state the definitions of a topological space, a basis, a closed set, a continuous function and a homeomorphism
- will be able to explain the product and metric topologies with their properties
- will be able to explain the compactness of a topological space
- will be able to explain the connectedness of a topological space and the differences between the connectedness and path connectedness
- will be able to explain the countability and separation axioms
- will be able to compare the topological spaces with the help of countability and separation axioms
- will be able to explain the quotient topology and its properties
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution