2022 Exercises in Set and Topology I

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Gotoda Takeshi  Murofushi Toshiaki  Miura Hideyuki  Suzuki Sakie  Umehara Masaaki  Tsuchioka Shunsuke  Takahashi Jin  Ichiki Shunsuke  Nishibata Shinya 
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Exercise    (Livestream)
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Course description and aims

This course is offered simultaneously with the lecture "MCS.T201: Set and Topology I" and provides exercises on set theory and metric space.
The aim of this course is to understand the fundamentals of set theory and metric space well and apply them to practical problems.

Student learning outcomes

The students are expected to understand important examples of set theory and metric space, to learn the fundamentals to handle mathematical subjects rigorously and also to be able to apply them to practical problems.


Set, Map, Family of Sets, Axiom of Choice, Equivalence Relation, Quotient Set, Cardinality, Order Relation, Well-ordered set, Metric Space

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.T201 : Set and Topology I". The students are strongly encouraged to register for "MCS.T201 : Set and Topology I".

Course schedule/Required learning

  Course schedule Required learning
Class 1 Set and Set Operation report1
Class 2 Map, Family of Sets, Axiom of Choice report2
Class 3 Equivalence Relation and Quotient Set report3
Class 4 Cardinality report4
Class 5 Countable Set/Uncountable Set, Cardinality of the Continuum report5
Class 6 Order Relation, Well-Ordered set, Zorn's lemma report6
Class 7 Euclidean Space and 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.


"Set and Topological Space (in Japanese)" by Shigeyuki Morita published by Aasakura Shoten.

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. Details will be announced in the first lecture.

Related courses

  • MCS.T201 : Set and Topology I

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

The students who register for this course are strongly encouraged to do for "MCS.T201: Set and Topology I" simultaneously.

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