MATH571 TOPOLOGICAL VECTOR SPACES
| Course Code: | 2360571 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. ÖZCAN YAZICI |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of the course, students are expected to learn
- basic properties of linear topological spaces
- completion and metrizability
- locally convex topological vector spaces
- Hahn-Banach Theorems
- projective and inductive limits
- Krein-Milman Theorem
- Frechet spaces, bases in Frechet spaces
- linear topological invariants.
Course Content
Introduction to topological vector spaces, locally convex topological vector spaces. Inductive and projective limits. Frechet spaces. Montel, Schwartz, nuclear spaces. Bases in Frechet spaces and the quasi-equivalence property. Köthe sequence spaces. Linear topological invariants.
Course Learning Outcomes
After successfully completing this course, students will be able to:
- define and explain key concepts in linear topological spaces.
- define completion and metrizability.
- work with locally convex topological vector spaces.
- apply Hahn-Banach Theorems to separate convex sets.
- work with projective and inductive limits.
- use the tools of Frechet spaces and construct bases in Frechet spaces.
- define some linear topological invariants.
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 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 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 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 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