Ders Planı

Lesson Information

Course Credit	3.0
Course ECTS Credit	5.0
Teaching Language of Instruction	Türkçe
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Programme Elective
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	S
Course Coordinator
Instructor (s)	Prof. Dr. ÇİĞDEM GENCER BALBİANİ
Course Assistant	Prof. Dr. İSMAİL TOK

Purpose and Content

The aim of the course	The aim of this course is to give the knowledge about the basic concepts of topological spaces.
Course Content	This course covers metric spaces. Topological spaces. basis, subbasis, subspaces. Closed sets, Neighborhood ,Limit, interior and boundary points. The notion of convergence. Continuous functions, homeomorphisms, Product and quotient spaces. Lindelof, first and second countable spaces. Seperable spaces. Separation axioms. T_0 , T_1 and Hausdorff spaces. Regular and normal spaces. Urysohn s and Tietze s theorems. Compact spaces. Connected spaces. Topological groups.

The aim of the course

The aim of this course is to give the knowledge about the basic concepts of topological spaces.

Course Content

This course covers metric spaces. Topological spaces. basis, subbasis, subspaces. Closed sets, Neighborhood ,Limit, interior and boundary points. The notion of convergence. Continuous functions, homeomorphisms, Product and quotient spaces. Lindelof, first and second countable spaces. Seperable spaces. Separation axioms. T_0 , T_1 and Hausdorff spaces. Regular and normal spaces. Urysohn s and Tietze s theorems. Compact spaces. Connected spaces. Topological groups.

Learning Outcomes

Have advanced theoretical and practical knowledge in mathematics and computer science.
Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, accessing the internet and softwares.
Possess the knowledge of advanced research methods in mathematics-computer field.
Possess theoretical and practical knowledge in mathematics, computation and computer science.
Define computer programming, word processing, data functions, internete access and software programs.
Describe advanced research methods in the field of Mathematics-Computer Science.
Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.
Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence.
Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose.
Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and evaluate these environments.
Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.
Perform all phases of life cycle in computer based systems.
Work effectively as an individual and as a team member to solve problems in the areas of mathematics and computer science.
Have the ability to act independently, use initiative and creativity.
Work effectively either individually or in multidisciplinary teams.
Evaluate advanced knowledge and skills in the field with a critical approach.
Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.
Have the consciousness of the necessity of lifelong learning and continuously develop professional knowledge and skills.
Use the time effectively in the process of getting the conclusion with analytical thinking ability.
Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.
Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation.
Have the awareness of professional and ethical responsibility and legal consequences of information applications
Use the knowledge about the field for the benefit to society.

Weekly Course Subjects

1	Metric spaces.
2	Open, closed sets, and continuity iin metric spaces.
3	Topological spaces. basis, subbasis, subspaces.
4	Neighborhood ,Limit, interior and boundary points. The notion of convergence.
5	Continuous functions and homeomorphism.
6	Construction of topological spaces: subspaces, product, and quotient spaces.
7	Countability axioms,Lindelof, first and second countable spaces.
8	Seperable spaces. Separation axioms.
9	T_0 , T_1 and Hausdorff spaces.Midterm Exam.
10	Regular and normal spaces.
11	Urysohn s and Tietze s theorems.
12	Compactness, sequential compactness, compactification, separation axioms.
13	Connectedness,connected components,path conncetednes, path components.
14	Topological groups.

Resources

1-James R. Munkres , Topology, 2nd Edition.
2- Cemil Yüksel,Genel Topoloji.
3- Saziye Yuksel, Genel Topoloji.
4-Timur Karaçay, Genel Topoloji.

CLASS 1

CLASS 2

CLASS 3

CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources