1  Course Title:  TOPOLOGY 
2  Course Code:  MAT3018 
3  Type of Course:  Compulsory 
4  Level of Course:  First Cycle 
5  Year of Study:  3 
6  Semester:  6 
7  ECTS Credits Allocated:  6 
8  Theoretical (hour/week):  2 
9  Practice (hour/week) :  2 
10  Laboratory (hour/week) :  0 
11  Prerequisites:  none 
12  Recommended optional programme components:  None 
13  Language:  Turkish 
14  Mode of Delivery:  Face to face 
15  Course Coordinator:  Prof. Dr. OSMAN BİZİM 
16  Course Lecturers: 
Prof. Dr. Osman Bizim 
17  Contactinformation of the Course Coordinator: 
Uludağ Üniversitesi, FenEdebiyat Fakültesi Matematik Bölümü, Görükle BursaTÜRKİYE 0 224 294 17 50 / obizim@uludag.edu.tr 
18  Website:  
19  Objective of the Course:  The aim of the course is to make the students gain the basic subjects of the topological spaces. The goals are to teach the topological spaces, examples of topological and the related notions and results so that the students can make their applications, and let them know about the historical background of the topics. 
20  Contribution of the Course to Professional Development 
21  Learning Outcomes: 

22  Course Content: 
Week  Theoretical  Practical 
1  Topology, topological space and subspace topology  Examples of the Topology, topological space, subspace topology 
2  Topological concepts, interior and exterior points, boundary points, accumulation points and closure points in topological space.  Examples of the Topological concepts, interior and exterior points, boundary points, accumulation points and closure points in topological space. 
3  Base, subbase and local base of the topology.  Examples of the Base, subbase and local base of the topology. 
4  The countable space and the separable space  Examples of The countable space and the separable space. 
5  The neighborhoods in the topological spaces and the system of the neighborhoods.  Examples of the neighborhoods in the topological spaces and the system of the neighborhoods. 
6  Continuous functions on topological spaces.  Examples of the continuous functions on topological spaces and properties of continuous functions. 
7  Open and closed functions, homeomorphisms on topological spaces.  Examples of the Open and closed functions, homeomorphisms on topological spaces. 
8  Sequences in the topological spaces, convergent sequences, nets and filters.  Examples of the Sequences in the topological spaces, convergent sequences, nets and filters. 
9  Product topology and the properties of the product spaces.  Examples of the product spaces. 
10  Quotient topology and the properties of the quotient spaces.  Examples of the quotient spaces. 
11  Compact topologic spaces and their properties, countable and sequential compact topologic spaces.  Examples of the compact topologic spaces. 
12  Local compact spaces and one point compactification.  Examples of the local compact spaces and one point compactification. 
13  Connected topologic spaces, path connected spaces, meanvalue theorem and local connected spaces.  Examples of the connected topologic spaces, path connected spaces and local connected spaces. 
14  The separation axioms in topological spaces and metrizable spaces  Properties of the separation axioms in topological spaces 
23  Textbooks, References and/or Other Materials: 
[1] Topoloji, O. Bizim [2] Topoloji, O. Mucuk [3] Genel topoloji, N. Yıldız [4] Topology, J. Munkers 
24  Assesment 
TERM LEARNING ACTIVITIES  NUMBER  PERCENT 
Midterm Exam  1  40 
Quiz  0  0 
Homeworks, Performances  0  0 
Final Exam  1  60 
Total  2  100 
Contribution of Term (Year) Learning Activities to Success Grade  40  
Contribution of Final Exam to Success Grade  60  
Total  100  
Measurement and Evaluation Techniques Used in the Course  
Information 
25  ECTS / WORK LOAD TABLE 
Activites  NUMBER  TIME [Hour]  Total WorkLoad [Hour] 
Theoretical  14  2  28 
Practicals/Labs  14  2  28 
Self Study and Preparation  14  4  56 
Homeworks, Performances  0  0  0 
Projects  0  0  0 
Field Studies  0  0  0 
Midtermexams  1  15  15 
Others  14  2  28 
Final Exams  1  25  25 
Total WorkLoad  180  
Total workload/ 30 hr  6  
ECTS Credit of the Course  6 
26  CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS  

LO: Learning Objectives  PQ: Program Qualifications 
Contribution Level:  1 Very Low  2 Low  3 Medium  4 High  5 Very High 