| Academic Year |
2025Year |
School/Graduate School |
International Institute for Sustainability with Knotted Chiral Meta Matter (Courses for Graduate Students) |
| Lecture Code |
8K200101 |
Subject Classification |
Specialized Education |
| Subject Name |
Introduction to topology |
Subject Name
（Katakana） |
イントロダクション トゥ トポロジー |
Subject Name in
English |
Introduction to topology |
| Instructor |
KODAMA HIROKI,KOTORII YUKA |
Instructor
(Katakana) |
コダマ ヒロキ,コトリイ ユウカ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Mon3-4,Fri3-4：SCI B305 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Use blackboard. |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
E
:
English |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
For students registered International Program for Collaborative Sciences Enabling the Future |
| Keywords |
topology, group theory |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
This course is a rigorous introduction to general topology (point set topology). We start from the set theory and introduce topology on a set. We discuss continuous mappings between topological spaces and further standard topics on topological spaces. These will be necessary to understand the fundamental groups and higher homotopy groups to describe topological defects. |
| Class Schedule |
lesson1 Sets (Hiroki Kodama)
lesson2 Mappings (Hiroki Kodama)
lesson3 Equivalence relation and equivalence class (Hiroki Kodama)
lesson4 Cardinality: countable and uncountable sets (Hiroki Kodama)
lesson5 Ordering (Hiroki Kodama)
lesson6 Metric spaces (Hiroki Kodama)
lesson7 Topology and topological spaces (Hiroki Kodama)
lesson8 Base and subbase (Hiroki Kodama)
lesson9 Continuous mappings and homeomorphisms (Hiroki Kodama)
lesson10 Derived concepts (Hiroki Kodama)
lesson11 Product topology and subspace (Hiroki Kodama)
lesson12 Quotient topology, separation axioms (Hiroki Kodama)
lesson13 Compactness and connectedness (Hiroki Kodama)
lesson14 Groups, subgroups and normal subgroups (Hiroki Kodama)
lesson15 Group homomorphisms and their properties (Hiroki Kodama) |
Text/Reference
Books,etc. |
References: (1) J. Munkres, Topology, Pearson (2) J. Kelly, General topology, Springer (3) S. Willard, General topology, Courier Corp. |
PC or AV used in
Class,etc. |
|
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
No need to prepare before each lecture, but you are expected to review after each lecture. Often, we will assign exercises. |
| Requirements |
|
| Grading Method |
Based on the understanding of contents (100%). |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |