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Course Information
Course Unit Title : Topology II
Course Unit Code : MAT310
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 3
Semester : 6.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) :
Course Assistants :
Learning Outcomes of The Course Unit : Quotient spaces, product spaces, convergence, seperation axioms, kompactness and connectivity.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Quotient Spaces: Strong topologies, quotient maps and spaces, quotient spaces from equivalence relations and examples.
Product Spaces: Topologies on product of sets and various examples, projections and their topological properties.
Convergence: The notion of convergence in topological spaces and examples.
Seperation Axioms: Hausdorff , regular and normal spaces, seperation axioms in metric and Euclidean spaces, Urysohn and Tietze characterizations of normality.
Compact Spaces: Compact spaces, examples of compact and non-compact spaces, Tychonoff `s theorem, boundedness of real valued functions.
Connected Spaces: Connected spaces and examples, connectedness in Euclidean spaces, path connected spaces and Jordan`s closed curve theorem.
Languages of Instruction : Turkish-English
Course Goals : To carry out some notions from Euclidean spaces such as convergence, connectivity, etc, to topological spaces and to describe topologies on product of sets.
Course Aims : To carry out some notions from Euclidean spaces such as convergence, connectivity, etc, to topological spaces and to describe topologies on product of sets.
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 Product Spaces: definition and examples.
 
2 Continuity in product spaces.
 
3 Strong topologies and quotient spaces.
 
4 Convergence in topological spaces: defininitions.
 
5 Convergence in topological spaces: chracterizations.
 
6 Convergence and continuity.
 
7 Seperation Axioms: T_0, T_1 and T_2-spaces.
 
8 Seperation Axioms: T_3 and T_4 spaces.
 
9 Seperation Axioms: Urysohn and Tietze?s theorems.
 
10 Compact spaces: definitions and examples.
 
11 Compact spaces and seperation axioms.
 
12 Connectivity in topological spaces.
 
13 Path connected spaces.
 
14 Review and conculusions.