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Course Information

Course Name
Turkish Topoloji
English Topology
Course Code
MAT 605 Credit Lecture
Semester 1
3 3 - -
Course Language Turkish
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.
Required Facilities
Textbook 1.. Munkres, J.R. (2000). Topology, A first Course, Upper Saddle River, NJ Prentice, Hall, Inc..
Other References
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