Information Package / Course Catalogue
Topology
Course Code: MTK505
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

The purpose of this course is to introduce students to the topics in the course content.

Course Content

Basic concepts, bases, subbases and local bases, closure, interior, boundary, product spaces, quotient spaces, continuity, separation axioms, sequences and nets, metric spaces, complete metric spaces, compactness, connectedness.

Name of Lecturer(s)
Prof. Adnan MELEKOĞLU
Learning Outcomes
1.Ability to determine the topology by means of a base or subbase
2.Ability to define continuous and discontinuous functions between topological spaces
3.Ability to determine the points that a sequence or a net converges in a topological space
4.Ability to determine the topology generated by a metric
5.Ability to explain the concepts of compactness and connectedness and their relations with other topological concepts
Recommended or Required Reading
1.M. Koçak, Introduction to General Topology and Solved Problems, Nisan Publ., 2020.
2.J. R. Munkres, Topology, Prentice Hall, 2000.
Weekly Detailed Course Contents
Week 1 - Theoretical
Bases, subbases and local bases
Week 2 - Theoretical
First and second countable spaces
Week 3 - Theoretical
Closure, interior and boundary
Week 4 - Theoretical
Product spaces
Week 5 - Theoretical
Quotient spaces
Week 6 - Theoretical
Continuous functions
Week 7 - Theoretical
Homeomorphisms
Week 8 - Theoretical
T0, T1 and Hausdorff spaces, Midterm exam
Week 9 - Theoretical
Regular, completely regular and normal spaces
Week 10 - Theoretical
Sequences and nets
Week 11 - Theoretical
Metric spaces
Week 12 - Theoretical
Complete metric spaces
Week 13 - Theoretical
Compactness
Week 14 - Theoretical
Connectedness
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Individual Work1408112
Midterm Examination118220
Final Examination124226
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
1
1
3
2
1
OÇ-2
3
1
1
3
2
1
OÇ-3
3
1
1
3
2
1
OÇ-4
3
1
1
3
2
1
OÇ-5
3
1
1
3
2
1
Adnan Menderes University - Information Package / Course Catalogue
2026