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Course Information
Course Unit Title : Topology I
Course Unit Code : MAT309
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 3
Semester : 5.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) :
Course Assistants :
Learning Outcomes of The Course Unit : Topological spaces, continuity, homeomorphisms, topological properties.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : What is topology?: History and developments of topology, Euclidean spaces and geometric properties revised.
Metric Spaces: The metric functions and spaces, interior and closure operators, convergence and continuity in metric spaces.
Topological Spaces: Definitions and examples of topological spaces, interior and closure operators, neighbors, subspaces.
Bases: Bases and subbases, the first and second countable spaces, seperable spaces.
Continıity: Definition and examples of continuity in topological spaces, homeomorphisms and topological properties.
Weak Topologies: Topologies determined by functions.
Languages of Instruction : Turkish-English
Course Goals : To develop an understanding of continuity that does not depend on distances, and to explain properties preseved by continious maps and clasify spaces under homeomorphisms.
Course Aims : To develop an understanding of continuity that does not depend on distances, and to explain properties preseved by continious maps and clasify spaces under homeomorphisms.
WorkPlacement   Not Available
Recommended or Required Reading
Textbook :
Additional Resources : i-)Bülbül, A., ?Genel Topoloji?, Hacettepe Ün. Yayınları, 2004.
ii-) Joshi, K.D. Introduction to General Topology, Wiley-Eastern Limited, 1983.
iii-) Willard, S. General Topology, Addison-Wesley, 1970.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
15 4 60  
Homeworks :
3 15 45  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 15 15  
Finals :
1 15 15  
Workload Hour (30) :
30  
Total Work Charge / Hour :
177  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 15
Quiz :
0 0
Homework :
3 15
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
30
The ratio of the term to success :
40
The ratio of final to success :
60
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 General description and a short history of point-set topology.
 
2 Euclidean topologies, metrics and examples.
 
3 Set-operators in metric spaces.
 
4 Continuity and convergence in metric spaces.
 
5 Topological spaces: defintions and examples, closure and interior, ect.
 
6 Subspaces
 
7 Bases in topological spaces.
 
8 Characterizations and examples.
 
9 Generating new topologies and subbases.
 
10 A_1 and A-2-spaces: examples.
 
11 Seperable spaces: examples.
 
12 Continuity in topological spaces.
 
13 Open and closed functions, homeomorphisms.
 
14 Weak topologies and examples.