Topology 1(위상수학 개론 1)

The purpose of this course is to introduce the concept of topology, topological spaces, and continuity. Topology was revolutionary in the early 20th century providing many
new ideas in various parts of mathematics.

Topology will play basic roles in analysis, algebra, and differential geometry. It serves as a foundation so one must become fairly comfortable with point-set topology in order to succeed in undergraduate and graduate education. Even in many areas of applied mathematics, topology appears often in disguised or undisguised forms.

We will introduce topological spaces, metric spaces, continuity, and various separation properties of topological spaces, i.e., Hausdorff property, regularity, normality, etc. We will discuss connectedness, compactness, sequences, separation properties, metrizations, quotient topology, function spaces and compact open topology. We will examine examples of topological spaces and constructions of topological spaces.

Also, there is a topology exam in the entrance examination for MS and Ph.D. degrees
as well as a qualifying exam at MS level in topology which you must pass.

Basic Text books are Munkres, "Topology, an introduction" and
Kahn, "Introduction to point-set topology and algebraic areas."

 

시간: 화목: 10:30-11:45 장소: 056-218

2004I 조교:

전우진: 연구실 27동 318호, 전화: 6272,  이메일: j_woojin@hanmail.net

           면담시간: 목 4-5시

마대건: 연구실: 27동 321호, 전화: 1316, 이메일: madgun@dreamwiz.com

           면담시간: 화 1-2시

Office: 27-317C

e-mail: shchoi@math.snu.ac.kr

Phone: 880-8169

Exams: midterm and final

Reports: 4 times or so

Grades: Midterm 25 pts, Final 35 pts, Report 30 pts, Participation 10pts

 

2004 1학기 성적

 

 

주

날짜

 강의 계획

 비고

 1

3월2,4

 Set theory, metric spaces

 

 2

3월9,11

 Topology, interior, boundary, bases

 

 3

3월16,18

 subbases, order topology, product topology

 

 4

3월23,25

 Continuous functions, Hausdorff topology

 

 5

3월30.4월1

 Metric topology

 

 6.

4월 6,8

 Compact spaces, Tyconoff theorem

 

 7

4월 13,15

 Connected spaces

 

 8

4월 20,22

 Quotient topology

중간 고사 22일

 9

4월 27,29

 Quotient topology

 

 10

5월 4,6

 Separation properties

 

 11

5월 11,13

 Separation properties

 

 12

5월 18,20

 Stone-Cech compactifications

 

 13

5월 25, 27

 Metrization theorem

 

 14

6월 2, 4

 Complete metric spaces and function spaces

 

 15

6월 8.10.

 기말고사 10일