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MAT 605
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Course Information
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Course Information
Course Name
Turkish
Topoloji
English
Topology
Course Code
MAT 605
Credit
Lecture
(hour/week)
Recitation
(hour/week)
Laboratory
(hour/week)
Semester
1
3
3


Course Language
Turkish
Course Coordinator
İbrahim Kırat
Course Objectives
1. To teach some of the highlevel 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 CompactOpen 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.
Prerequisite(s)
Required Facilities
Other
Textbook
1.. Munkres, J.R. (2000). Topology, A first Course, Upper Saddle River, NJ Prentice, Hall, Inc..
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