2016 Exercises in Set and Topology II

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Murata Miho  Murofushi Toshiaki  Takasawa Mitsuhiko 
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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. This course is held once per week for seven or eight weeks since its credit is one.

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


"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. 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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