2025 (Current Year) Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science
Set and Topology II
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Toshiaki Murofushi / Masaaki Umehara / Shunsuke Tsuchioka / Sakie Suzuki
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon (W8E-307(W833)) / 3-4 Thu (W8E-307(W833))
- Class
- -
- Course Code
- MCS.T221
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Oct 9, 2025
- Language
- Japanese
Syllabus
Course overview and goals
The set and topology play an important role in mathematical and computing science. The objective of this course is to explain the fundamentals of the point set topology based on the knowledge about set provided in "Set and Topology I" in the first quarter, and also for the students to built backgrounds to apply the idea of point set topology in mathematical and computing science.
Course description and aims
The students are expected to understand the fundamentals of mathematical methods to handle topological structure appeared in mathematical and computing science and also to be able to apply them to practical problems.
Keywords
topology, topological space, neighborhood, continuous, Hausdorff space, separation axioms, connected, compact, complete
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The lectures provide the fundamentals of the point set topology. The students are strongly encouraged to register for "MCS.T222：Exercises in Set and Topology II" simultaneously which offers the recitation session for this course.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Metric Spaces |
Understand the contents covered by the lecture. |
| Class 2 | Topological Spaces |
Understand the contents covered by the lecture. |
| Class 3 | Subsets of Topological Spaces |
Understand the contents covered by the lecture. |
| Class 4 | Relative Topology and Continuous Maps |
Understand the contents covered by the lecture. |
| Class 5 | Product Topology |
Understand the contents covered by the lecture. |
| Class 6 | Separation Axioms I |
Understand the contents covered by the lecture. |
| Class 7 | Separation Axioms II |
Understand the contents covered by the lecture. |
| Class 8 | Connectivity |
Understand the contents covered by the lecture. |
| Class 9 | Compactness I |
Understand the contents covered by the lecture. |
| Class 10 | Compactness II |
Understand the contents covered by the lecture. |
| Class 11 | Compactification |
Understand the contents covered by the lecture. |
| Class 12 | Completeness of Metric Space I |
Understand the contents covered by the lecture. |
| Class 13 | Completeness of Metric Space II |
Understand the contents covered by the lecture. |
| Class 14 | completion of metric spaces |
Understand the contents covered by the lecture. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Korekara no Syuugou to Isou (by Profs. Umehara and Ichiki), Shokabo
Reference books, course materials, etc.
None
Evaluation methods and criteria
By score of the final examination. If you register for "MCS.T222:Exercises in Set and Topology II", its score will be counted as a part of contributions also. Details will be announced in the first lecture.
Related courses
- MCS.T201 ： Set and Topology I
- MCS.T202 ： Exercises in Set and Topology I
- MCS.T222 ： Exercises in Set and Topology II
Prerequisites
The students are encouraged to take "MCS.T201：Set and Topology I" and "MCS.T202：Exercises in Set and Topology I" before registering for this course. Also, those who register for this course are strongly encouraged to do for "MCS.T222：Exercises in Set and Topology II" simultaneously.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
MUROFUSHI, Toshiaki (murofusi[at]gmail.com)
Office hours
To be announced in the first lecture.