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| MAT5150 | Advanced Topology | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Tane VERGİLİ | | Co-Lecturer | Assistant Professor Seda Öztürk | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To cover basic concepts of point set topology and to gain the ability to apply these concepts to provided topological problems.
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| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | recall the basic definitions of point-set topology accurately. | 1,4 | 1,3,6 | | PO - 2 : | write out proofs of the simpler theorems and propositions. | 1,4 | 1,3,6 | | PO - 3 : | apply their knowledge to examples of specific topological and metric spaces. | 1,4 | 1,3,6 | | 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), PO : Learning Outcome | | |
| Sets and Functions, Topological Spaces and Continuous maps, Homeomorphism, Product and Quotient Spaces, Metric Spaces, Counttability and Separation Axioms, Compactness, Connected and Path Connected Spaces, Compactification and Paracompactness, Baire Spaces
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Sets, operations with sets, functions, relations,
| | | Week 2 | Topological space, basis for a topology, order topology and topology examples on R
| | | Week 3 | Subspace Topology, neighborhood of a point, closure and cluster points | | | Week 4 | Product Spaces and Quotient Spaces
| | | Week 5 | Continuity, open and closed functions, homeomorphism | | | Week 6 | Countability, first and second countable spaces, separable spaces | | | Week 7 | Separation Axioms: T_0, T_1, and T_2 spaces | | | Week 8 | Mid-term exam | | | Week 9 | Separation Axioms: normal and regular spaces, T_3 and T_4 spaces | | | Week 10 | Compactness and local compaktness, sequentially compactness, Extreme Value Theorem
| | | Week 11 | Connected Spaces, Intermediate Value Theorem, Path Connected Spaces
| | | Week 12 | Metric Spacers, Urysohn's Lemma, Tietze Extension Theorem
| | | Week 13 | One-point (Alexandroff) compactification, Tychonoff Spaces
| | | Week 14 | Stone-Cech compactification | | | Week 15 | Paracompactness and Baire Spaces | | | Week 16 | End-of-term exam | | | |
| 1 | Munkres, James R. 2000;Topology. Second edition, Prentice-Hall Inc.,Englewood Cliffs, N.J., | | | |
| 1 | Runde,Volker .2005; A Taste of Topology, Universitext. Springer Verlag, | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | - | 2 | 30 | | Quiz | 12 | - | 2 | 20 | | End-of-term exam | 16 | - | 2 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 7 | 14 | 98 | | Arasınav için hazırlık | 10 | 2 | 20 | | Arasınav | 2 | 1 | 2 | | Ödev | 4 | 4 | 16 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 3 | 1 | 3 | | Total work load | | | 196 |
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