2022 Exercises in Set and Topology II

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Murofushi Toshiaki  Tsuchioka Shunsuke  Ichiki Shunsuke  Umehara Masaaki 
Class Format
Exercise    (Face-to-face)
Media-enhanced courses
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Course description and aims

This course is offered simultaneously with the lecture "MCS.T221:Set and Topology II" and provides exercises on the point set topology. The aim of this course is to understand the fundamentals of the point set topology well and apply them to practical problems.

Student learning outcomes

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.


topology, topological space, neighborhood, continuous, Hausdorff space, separation axioms, connected, compact, complete

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

The lectures provide exercises on topics of "MCS.T221:Set and Topology II". The students are strongly encouraged to register for "MCS.T221:Set and Topology II".

Course schedule/Required learning

  Course schedule Required learning
Class 1 Euclidean Space, Metric Space Report1
Class 2 Topological Space, Basis and Neighborhood System Report2
Class 3 Continuous Map, Induced Topology Report3
Class 4 Product Topology, Hausdorff Space Report4
Class 5 Normal Space, Regular Space, Separation Axiom Report5
Class 6 Connectivity, Compactness Report6
Class 7 Completeness and Completion of Metric Space Report7

Out-of-Class Study Time (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.


Naive Set Theory and General Topology ---the Empty Set as a Companion--- (in Japanese), Masaaki Umehara and Shunsuke Ichiki, Shokabo, to be published in November.

Reference books, course materials, etc.

The person in charge will hand out materials accordingly.

Assessment criteria and methods

By scores of reports and class performance. If you register for "MCS.T221: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.T221 : Set and Topology II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

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.T221:Set and Topology II" simultaneously.

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