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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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