Course Name	Topology II
Credits	3
Professor(s)	Name	Young Bae Jun
	Department	Department of Mathematics Education

COURSE DESCRIPTION

Course Objectives

Based on the basic concepts which are covered in the first semester, this lecture contains what I consider to be the bare essentials every student should know before beginning the study of complete metric spaces and function spaces, moreover, continum theory, set-theoretic topology, algebraic topology, functional analysis, or any of the many areas of mathematics that use topology in an important way. In this lecture, every student will make study of Separation Axioms, Compactness, Product Spaces, and Connectedness.

MAIN TEXTBOOK and FURTHER READINGS

Main Textbook:

-S. Lipschutz, Theory and Problems of General Topology,   McGraw-Hill Book. Co.,(1965).

Further Reading:

-S. W. Davis, Topology, McGraw-Hill Book. Co., (2005).

-M. C. Gemignani, Elementary Topology (2nd edition), Addison-Wesley Pub. Co. (1967).

ASSIGNMENTS AND GRADING

Assignments:

- To solve Exercises in each subject (Solving problems and submitting reports)

- To make a new problem from old one (Solving new problems).

Grading Scheme:

- Attendance and Assignments : 10%

- First Exam : 20%

- Second Exam (Mid-term Exam) : 25%

- Third Exam  : 20%

- Fourth Exam (Final Exam) : 25%

COURSE SCHEDULE

Course Outline

Week 1 : T1-space, Hausdorff space, Regular space.

Week 2 : Normal space, Urysohn's lemma and metrization problem.

Week 3 : Functions that separate points, Completely regular space.

Week 4 : Compact sets, Subsets of compact space. First Exam.

Week 5 : Finite intersection property, Compactness and Hausdorff space.

Week 6 : Sequentially compact sets, Countably compact sets.

Week 7 : Locally compact space, Compactifications.

Week 8 : Compactness in metric space, Totally bounded sets. Mid-term Exam.

Week 9 : Product topology, Base for a finite product topology.

Week 10 : Defining subbase for the product topology.

Week 11 : Defining base for the product topology.

Week 12 : Metric product space, Cantor sets. Second Exam.

Week 13 : Separate sets, Connected sets and spaces,

Connectedness on the real line.

Week 14 : Components, Locally connected space, Paths.

Week 15 : Arcwise connected sets, Homotopic paths, Final Exam.

CONTACT DETAILS

Tel.: +82 55 772 2254

e-mail : ybjun@gnu.ac.kr