Math 420 Elementary Point Set Topology Fall 2022

webpage:https://users.metu.edu.tr/beyaz/420/ Last updated September 30, 2022
Check frequently: https://metuclass.metu.edu.tr/

Tentative Schedule (Subject to Change):
1-Preliminaries
2-Topological Spaces, Basis
3-Examples, Product topology, Subbasis
4-Subspaces, Closed sets
5-Limit points. Hausdorff Spaces. (Exam 1)
6-Continuous functions, homeomorphisms
7-Metric topology
8-Quotient topology, Connected spaces
9-Components, path connectedness, path components
10-Compactness, local compactness. (Exam 2)
11-Countability axioms. Sequential compactness, compactness in metric spaces
12-Seperation axioms. Definition of regular and normal spaces. Urysohn's Lemma
13-Urysohn's Lemma, Tietze Extension Theorem
14-Additional topics

Suggested problems

Textbook:
 Topology - A First Course, J.R. Munkres, Prentice Hall, 2000.
Some Sources:
 Elements of Point Set Topology, J.D. Baum, Dover Publications.
Topology - An Introduction to the Point-Set and Algebraic Areas, D.W. Kahn, Dover Publications.
General Topology, J.L. Kelley, Springer.
Counterexamples in Topology, L.A. Steen, J.A. Seebach, Dover Publications.
TMD Matematik Dünyası Dergisi 2009

Grading:
Exam 1 (Nov 9, 17:30): 30%
Exam 2 (Dec 14, 17:30): 30%
Final: 40%
Lecture Time and Place:
Tuesday 12:40-13:30 M104
Thursday 13:40-15:30 M06
Office Hours:
Tuesday 13:40-15:30 M123
Catalog Description:
Topological Spaces; basis, subbasis, subspaces. Closed sets, limit points. Hausdorff Spaces. Continuous functions, homeomorphisms. Product topology. Connected spaces, compo-nents, path connectedness, path components. Compactness, sequential compactness, compactness in metric spaces. Definition of regular and normal spaces. Urysohn's Lemma, Tietsze Extension Theorem.
Prerequisites:
Math 251
**Make-up Exam: For students who have been unable to take any one of the exams for legitimate reasons (such as medical emergencies), a make-up exam will be offered. The make-up exam is usually harder than the final exam and takes place after it. The grade obtained at the make-up exam is then treated as the grade obtained in the exam that was missed.
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**Attendance will not be taken in this course.