Course Information

Course Name	Turkish	Topoloji
	English	Topology
Course Code	MAT 605E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	3	3	-	-
Course Language		English
Course Coordinator		İbrahim Kırat
Course Objectives		1. To teach some of the high-level topics of Topology, 2. To form the necessary background for the graduate students who wish to do research on Topology.
Course Description		Topological Spaces and Continuous Functions: Basis for a Topology, The Product Topology, The Metric Topology, The Quotient Topology. Connectedness and Compactness: Components and Path Components, Local Connectedness, Compact Spaces, Local Compactness. Countability and Separation Axioms, The Urysohn Metrization Theorem, The Tychonoff Theorem Metrization Theorems and Paracompactness: The Smirnov Metrization Theorem. Complete Metric Spaces and Function Spaces: The Compact-Open Topology, Ascoli’s Theorem, Baire Spaces.
Course Outcomes		A student completing this course succesfully is expected to have learned the topics: I. Topological Spaces and Continuous Functions , II. Connectedness and Compactness, III. Countability and Separation Axioms, IV. The Urysohn Metrization Theorem, V. The Tychonoff Theorem, VI. Metrization Theorems and Paracompactness , VII. Complete Metric Spaces and Function Spaces.
Pre-requisite(s)
Required Facilities
Other
Textbook		1. Munkres, J.R. (2000). Topology, A first Course, Upper Saddle River, NJ Prentice, Hall, Inc..
Other References		2. Deshpande, V. (1988). Introduction to topology, New Delhi: Tata McGraw-Hill. 3. Willard, S. (2004). General Topology, Dover Publications Inc.. 4. Kelley, J.L. (2008). General Topology, Ishi Press. 5. Dugundji, J. (1966). Topology, McGraw-Hill Companies.

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