Information Package / Course Catalogue
Metric Spaces
Course Code: MAT320
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 5
Objectives of the Course

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

Course Content

Basic concepts, subspaces, bounded subsets, open balls, open and closed sets, equivalent metrics, normed spaces, continuity, sequences, complete metric spaces, compactness, connectedness.

Name of Lecturer(s)
Learning Outcomes
1.Ability to determine open, closed, and bounded sets in metric spaces
2.Ability to determine the topology generated by a metric
3.Ability to define continuous and discontinuous functions between metric spaces
4.Ability to form convergent and divergent sequences in a metric space
5.Ability to form compact subspaces of a metric spaces
Recommended or Required Reading
1.M. Koçak, Introduction to General Topology and Solved Problems, Nisan Publ., 2020.
2.M. O Searcoid, Metric Spaces, Springer, 2007.
Weekly Detailed Course Contents
Week 1 - Theoretical
Basic concepts
Week 2 - Theoretical
Subspaces
Week 3 - Theoretical
Bounded subsets
Week 4 - Theoretical
Open balls
Week 5 - Theoretical
Open and closed sets
Week 6 - Theoretical
Equivalent metrics
Week 7 - Theoretical
Continuity
Week 8 - Theoretical
Isometries (Midterm Exam)
Week 9 - Theoretical
Normed spaces
Week 10 - Theoretical
Sequences
Week 11 - Theoretical
Cauchy sequences
Week 12 - Theoretical
Complete metric spaces
Week 13 - Theoretical
Compactness
Week 14 - Theoretical
Connectedness
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140228
Lecture - Practice140228
Individual Work143042
Midterm Examination111213
Final Examination112214
TOTAL WORKLOAD (hours)125
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
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
3
4
4
OÇ-2
3
3
4
4
OÇ-3
3
4
4
OÇ-4
3
4
4
OÇ-5
Adnan Menderes University - Information Package / Course Catalogue
2026