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| MAT3014 | General Topology | 4+0+0 | ECTS:7 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Doç. Dr. Tane VERGİLİ | | Co-Lecturer | Associate Professor Tane VERGİLİ
Assistant Professor Seda ÖZTÜRK | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to provide for the students an introduction to theory of metric and topological spaces, introduce the topological properties to classify spaces, and gain the ability to consider basic topological problems. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Understand terms, definitions and theorems related to topology | 1,3,5 | 1 | | LO - 2 : | Demonstrate knowledge and understanding of metric spaces. | 1,3,5 | 1 | | LO - 3 : | Use separation axioms, connectedness, compactness, and continuous functions to understand structure of topological spaces and create new topological spaces by using subspace, product and quotient topologies. | 1,3,5 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| The course focuses on the basic notions of topological spaces, open and closed sets, basis and sub basis for a topology, interior/closure/exterior of a set and neighborhood of a point, sub space topology, continuous functions between topological spaces, homeomorphisms, metric functions, topology induced by a metric, continuity between metric spaces, product and quotient spaces, countability, separation axioms, connectedness and compactness.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Topological spaces, open and closed sets | | | Week 2 | Basis for a topology | | | Week 3 | Interior and closure of sets, limit points, the boundary of a set | | | Week 4 | Subspace topology
| | | Week 5 | Continuous functions and homeomorphisms | | | Week 6 | Product topology
| | | Week 7 | Metric, metric spaces and continuity | | | Week 8 | Equivalent metric spaces, complete metric spaces | | | Week 9 | Mid-term examination
| | | Week 10 | Quotient topology | | | Week 11 | Separation axioms | | | Week 12 | Countability | | | Week 13 | Connected and path connected spaces | | | Week 14 | Compact spaces, locally compactness
| | | Week 15 | General review | | | Week 16 | Final examination | | | |
| 1 | Munkres, James Raymond. 2000; Topology (2nd Edition), Prentice Hall | | | |
| 1 | Karaca, İsmet. 2020; Teorik ve Uygulama Alanlarıyla Topoloji, Palme Yayınevi | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 18/04/2022 | 1 | 50 | | End-of-term exam | 16 | 08/06/2022 | 1 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 12 | 1 | 12 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 16 | 1 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 200 |
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