Ordu 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
FMA604	TOPOLOGY II	Compulsory	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

The aim of the course is • to gain the basic information necessary in the field of topology.

Name of Lecturer(s)

Yrd. Doç. Dr. Serkan KARATAŞ

Learning Outcomes

1	To have the ability and knowledge of the advanced level of related to the field and use it in a real learning environment.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Identical topology and Quotient Space: Identical topology and Identical Function (or Identical) • Characteristics features of Identification • Quotient Space and Canonical Function • Saturated sentences in the equivalence connected topological space and the closure and the Interior and the complement of saturated sentence • Paracompact spaces: Local Finite Family • Features of local finite sub-sentences family • Paracompactness of a compact space • A paracompact space which is being a Normal space View of a Paracompact space under continuous and closed functions • Paracompactness of Metric spaces • Filters: Filters Comparison • Basis of filter • Ultra filter • Necessary and sufficient condition for being ultra filter of a filter • Image and Inverse Image of a filter • Convergence of a filter • Continuous image of a convergent filter • The filter characterization of Compact Spaces

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Identical topology and Quotient Space: Identical topology and Identical Function (or Identical)
2	Characteristics features of Identification
3	Quotient Space and Canonical Function
4	Saturated sentences in the equivalence connected topological space and the closure and the Interior and the complement of saturated sentence
5	Saturated sentences in the equivalence connected topological space and the closure and the Interior and the complement of saturated sentence
6	Paracompact spaces: Local Finite Family, Features of local finite sub-sentences family
7	Paracompactness of a compact space
8	Midterm exam
9	A paracompact space which is being a Normal space
10	View of a Paracompact space under continuous and closed functions
11	Paracompactness of Metric spaces
12	Filters: Filters Comparison, Basis of filter, ultra fitler
13	Necessary and sufficient condition for being ultra filter of a filter
14	Image and Inverse Image of a filter, Convergence of a filter
15	Continuous image of a convergent filter, the filter characterization of Compact Spaces
16	Final exam

Recommended or Required Reading

Munkres, James R. 2000;Topology. Second edition, Prentice-Hall Inc.,Englewood Cliffs, N.J.,

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	14	6	84
Problem Solving	10	3	30
Self Study	14	4	56
Individual Study for Mid term Examination	10	4	40
Individual Study for Final Examination	8	4	32
TOTAL WORKLOAD (hours)			248

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1

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