Yozgat Bozok University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT546	INTRODUCTION TO TOPOLOGY-II	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

To teach the course content of Topology.

Name of Lecturer(s)

Dr.Öğr.Üyesi Hürmet Fulya AKIZ

Learning Outcomes

1	To learn the concepts of homeomorphism, and topological properties
2	To learn the concept of metric space
3	To learn the concepts of normed spaces and complete metric space
4	To learn the concept of product space and quotient space
5	To learn the methods to derive topology

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Compact spaces, Various characterizations of compactness, Inheritance and multiplicity of compactness, Sequential compact spaces, Countable compact spaces, Local compact spaces, Equivalence of compacting complexity types in metric spaces, Connected spaces, Connected components, Local connected spaces, Curves, Curved joint spaces, Networks and filters , Complete metric spaces and the completion of a metric space, Homotopy of curves, Simple connected spaces and basic groups

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Continuous functions
2	Open and closed functions
3	Homeomorphism, topological properties
4	Homeomorphism, topological properties
5	Metric spaces
6	Metric spaces
7	Metric topologies
8	MID-TERM EXAM
9	Equivalent metrics
10	The diameter of a set, distance between sets
11	Norm spaces
12	Initial and final topologies
13	Initial and final topologies
14	Product spaces and quotient spaces
15	Product spaces and quotient spaces
16	FINAL EXAM

Recommended or Required Reading

O. Mucuk. Topoloji ve Kategori. 2010.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Attending Lectures	14	4	56
Problem Solving	14	2	28
Self Study	14	4	56
Individual Study for Mid term Examination	4	5	20
Individual Study for Final Examination	4	5	20
TOTAL WORKLOAD (hours)			184

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

LO4

LO5

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High