Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
TOPOLOGY I	801500715030		3 + 0	3.0	8.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery	Oral presentation, answer-question, discussion, solving problems.
Course Coordinator
Instructors	Sevda SAĞIROĞLU PEKER
Assistants
Goals	Topology serves to lay the foundations for study in analysis, in geometry and in algebraic topology. The aim of this lecture is to give some of the topological notions which one typically needs during academic research and to present them such a way that improve the analytical thinking.
Course Content	Definition of a filter, base of a filter, ultrafilters, limit of a filter, limit of a function with respect to a filter. Quasi-compact spaces, Compactification, Sequentially Compact Spaces, Countable Compactness. Topology of a Metric Space, Compact Metric Spaces, Connected Metric Spaces, Complete Spaces and their relationships. Pointwise convergence and uniform convergence, Equicontinuous Spaces of Functions.
Learning Outcomes	1) Learns the notions of filters and it's fundamental properties. 2) Learns the notions of the quatient space. 3) Learns the Stone-Cech compactification. 4) Learns the complete and compact metric spaces and their relations. 5) Learns the function spaces and topologies defined on function spaces 6) Learns the notion of equicontinuous functions. 7) Learns the Ascoli Theorem.

Week	Topics	Teaching and Learning Methods and Techniques	Study Materials
1. Week	Filters and Fundamental Properties of Filters	Question Answer Problem Based Learning	Homework
2. Week	Ultrafilters	Question Answer Brainstorming	Homework
3. Week	Limit of a filter and limit of a function with respect to a filter	Question Answer Station	Homework
4. Week	Quatient Space	Question Answer Opinion Pool	Homework
5. Week	Characterizations of compact spaces with respact to filters	Problem Solving Speech Loop	Homework
6. Week	Sequentially compact spaces and countable compactness	Question Answer Station	Homework
7. Week	Compactification	Question Answer Opinion Pool	Presentation (Including Preparation Time)
8. Week	Stone-Cech Compactification	Lecture Brainstorming	Presentation (Including Preparation Time)
9. Week	Complete Metric Spaces and Compactness	Question Answer Six Hats Thinking	Presentation (Including Preparation Time)
10. Week	Functıon Spaces	Lecture Six Hats Thinking	Presentation (Including Preparation Time)
11. Week	Pointwise and compact convergence	Lecture Six Hats Thinking	Presentation (Including Preparation Time)
12. Week	Compact-open Topology	Question Answer Brainstorming	Presentation (Including Preparation Time)
13. Week	Equicontinuous Spaces of Functions	Question Answer Six Hats Thinking	Presentation (Including Preparation Time)
14. Week	Ascoli's Theorem	Question Answer Brainstorming; Opinion Pool; Panel	Presentation (Including Preparation Time)

Recommended Sources

Gustave Choquet, Topology. Academic Press, New York and London 1966.

J. Dugundji, Topology. Allyn and Bacon, Inc. Boston 1970.

James R. Munkres, Topology (A First Course). 1979

N. Bourbaki, General Topology. Springer-Verlag Berlin Heidelberg 1995.

Süzgeçlerle ilgili temel kavramlar(yardımcı içerik)

*DK = Course's Contrubution.

	0	1	2	3	4	5
Level of contribution	None	Very Low	Low	Fair	High	Very High

Event	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Total weeks*Hours per week)	14	3	42
Work Hour outside Classroom (Preparation, strengthening)	14	4	56
Homework	5	10	50
Midterm Exam	1	3	3
Time to prepare for Midterm Exam	1	30	30
Final Exam	1	3	3
Time to prepare for Final Exam	1	40	40
	1	3	3
	1	3	3
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course			30