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  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) : Prof.Dr. FİKRET KUYUCU

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