DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : General Topology Course Code : MT-503 Course Type : Compulsory Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Learning Outcomes of the Course : Defines first and second countable spaces Comprehends Product topology, weak topology and embedding theorems Understands convergence of a sequence, the net and filter in topological spaces, Establishes a relationship between convergence in analysis and topology. Can define Hausdorff, regular and normal spaces Understands the compact space and comprehends basic theorems about compact spaces. Understands the relationship between compactness and convergence. Improves the ability of abstract thinking. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To provide information about countability in topological spaces, product spaces, weak topologies, embedding, homeomorphism, convergence, separation axioms and compactness . Course Contents : Countability in topological spaces, product spaces, embedding theorems, convergence, separation axioms, compactness, local compactness. Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Review of some topological concepts. Sub-base and the concept of neighborhood. Review of the relevant pages from sources Narration and discussion 2 First and Second countable spaces. Separable spaces. Review of the relevant pages from sources Narration and discussion 3 Product spaces and weak topologies. Review of the relevant pages from sources Narration and discussion 4 Embedding theorems. Convergence of sequences. Sequential continuity. Review of the relevant pages from sources Narration and discussion 5 Nets and Convergence. Filters and convergence. Review of the relevant pages from sources Narration and discussion 6 Problem-solving. T0 and T1-spaces. Review of the relevant pages from sources Narration and discussion 7 T2 (Hausdorff), regular, T3-spaces. Review of the relevant pages from sources Narration and discussion 8 Mid-term exam topics discussed in the lecture notes and sources again Exam 9 Completely regular, normal spaces and Jhon´s Lemma. and T4-spaces. Review of the relevant pages from sources Narration and discussion 10 Tychonoff spaces and T4 spaces Review of the relevant pages from sources Narration and discussion 11 The compactness andthe finite intersection property, and the relationship between the compactness and convergence. Heine-Borel Theorem. Review of the relevant pages from sources Narration and discussion 12 Heine-Borel Theorem. The relationship between compactness and Hausdorff spaces. Review of the relevant pages from sources Narration and discussion 13 Fundamental properties of compact spaces. Review of the relevant pages from sources Narration and discussion 14 local compactness Review of the relevant pages from sources Narration and discussion 15 Consequences of local compactness Review of the relevant pages from sources Narration and discussion 16/17 Final exam topics discussed in the lecture notes and sources again Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Genel Topology, Stephan Willard, Addison-Wesley, 1970  Genel Topoloji, Ali Bülbül, Karadeniz Teknik Üniversitesi Yayınları, 1994. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 90     Homeworks/Projects/Others 1 10 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Aquires sufficient knowledge to enable one to do research over and above the undergraduate level 4 2 Learns theoretical foundations of his/her field thoroughly 3 3 Uses the knowledge in his/her field to solve mathematical problems 4 4 Proves basic theorems in different areas of Mathematics 1 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 4 6 Uses technical tools in his/her field 3 7 Works independently in his/her field requiring expertise 3 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 2 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 2 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 3 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 1 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 3 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 5 70 Assesment Related Works     Homeworks, Projects, Others 1 10 10     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 10 10 Total Workload: 142 Total Workload / 25 (h): 5.68 ECTS Credit: 6