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.
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
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
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|
|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|
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.
The person in charge will hand out materials accordingly.
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.
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.