Course Information

Course Name	Turkish	Topolojiye Giriş
	English	Intro. Topology
Course Code	MAT 355E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	6	3	3	-	-
Course Language		English
Course Coordinator		Sultan Erdoğan Demir Sultan Erdoğan Demir
Course Objectives		1. To make the generalizations of some topics from analysis, 2. To teach connection between topological spaces and metric spaces, 3. To teach fundamental topics in topological spaces.
Course Description		Metric spaces. Topological spaces. Neighborhood and some concepts of topology. Limit, interior and boundary points. The notion of convergence. Continuous functions . 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. Theorems of metrization.
Course Outcomes		Students completing this course will be able to : I. Generalize the fundamental concepts convergence and continuity from analysis to metric spaces, II. Define topological space using the fundamental theorem in metric space, III. Prove theorems concerning topological spaces, IV. Use the knowledge of fundamental topics of topological space in mathematical proofs and calculations, V. Think abstractly.
Pre-requisite(s)		MAT 102 MIN DD/ MAT 102E MIN DD/ MAT 104 MIN DD/ MAT 104E MIN DD/ MAT213 MIN DD/ MAT213E MIN DD
Required Facilities
Other
Textbook		J.R. Munkres, Topology
Other References		1. M.J. Gemignani, Elementary Topology, 1972, Addison-Wesley Publishing Company 2. J.L. Kelley, General Topology

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