8K200101 Introduction to topology

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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 KOTORII YUKA

Instructor
(Katakana) 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：ECON B159

Lesson Style Lecture Lesson Style
(More Details) 　

Use blackboard.

Credits 2.0 Class Hours/Week 　 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
lesson2 Mappings
lesson3 Equivalence relation and equivalence class
lesson4 Cardinality: countable and uncountable sets
lesson5 Ordering
lesson6 Metric spaces
lesson7 Topology and topological spaces
lesson8 Base and subbase
lesson9 Continuous mappings and homeomorphisms
lesson10 Derived concepts
lesson11 Product topology and subspace
lesson12 Quotient topology, separation axioms
lesson13 Compactness and connectedness
lesson14 Groups, subgroups and normal subgroups
lesson15 Group homomorphisms and their properties

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.

Academic Year	2024Year	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	KOTORII YUKA
Instructor (Katakana)	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：ECON B159
Lesson Style	Lecture	Lesson Style (More Details)
Use blackboard.
Credits	2.0	Class Hours/Week		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 lesson2 Mappings lesson3 Equivalence relation and equivalence class lesson4 Cardinality: countable and uncountable sets lesson5 Ordering lesson6 Metric spaces lesson7 Topology and topological spaces lesson8 Base and subbase lesson9 Continuous mappings and homeomorphisms lesson10 Derived concepts lesson11 Product topology and subspace lesson12 Quotient topology, separation axioms lesson13 Compactness and connectedness lesson14 Groups, subgroups and normal subgroups lesson15 Group homomorphisms and their properties
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.

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