Iğdır 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
MAT-23-114	ADVANCED TOPOLOGY I	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

Having an abstract idea on advanced topology topics Intelligence on advanced topology issues Conclusion about advanced topology

Name of Lecturer(s)

Dr. Öğr. Üyesi Alkan ÖZKAN

Learning Outcomes

1	To reinforce learning concepts of topological at undergraduate education
2	To obtain new topologies with existing topologies
3	Understand the relationships between topological spaces with metric spaces
4	To learn topology relationship with other branches of mathematics
5	To get information compact spaces and various compactness

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

none

Recommended Optional Programme Components

none

Course Contents

Sets and Functions, Partial and Equivalent Relations, Countable and Uncountable Cues, Partial Ranking Relationship and Perfect Order Relation, Metric Spaces, Closed and Open Codes, Convergence, Completeness and Baire Theorem, Continuous Transformations and Continuous Functions Spaces, Euclidean and Unit Spaces, Topological Spaces, Bases and Sub Bases, Weak Topologies, Compactness, Product Spaces, Tychonoff Theorem and Local Compact Spaces, Compactness in Metric Spaces, Separation Axioms, T1 and Hausdorff Spaces, Perfect Regular and Normal Spaces, Urysohn Lemması and Extended Tietze Theorem, Stone-Cech Compactification, Connectivity, A Comet of Space, Total Unconnected Spaces and Local Connected Spaces.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Preliminary
2	Topology of the Line and Plane
3	Bases and Subbases
4	Topological Continuity and Topological Equivalence
5	Metric Spaces
6	Metric Topology
7	Countability
8	Seperation Axioms
9	Topologies Induced by Functions
10	Product Spaces
11	Quotient Spaces
12	Compact Spaces
13	Various Compactness
14	Paracompakt Spaces

Recommended or Required Reading

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	1	1
Final Examination	1	1	1
Practice	14	1	14
Problem Solving	14	2	28
Discussion	14	1	14
Question-Answer	14	2	28
Team/Group Work	7	2	14
Brain Storming	14	1	14
Self Study	14	2	28
Report	7	2	14
Homework	14	1	14
TOTAL WORKLOAD (hours)			170

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO1	4	4	4	4	4	4	4	4	4	4	4
LO2	4	3	4	4	4	4	4	4	4	4	4
LO3	4	4	4	4	4	4	4	4	4	4	4
LO4	4	4	4	4	4	4	4	3	5	4	4
LO5	4	4	3	4	5	5	5	5	5	5	5

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