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.
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
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | Required learning | |
---|---|---|
Class 1 | Euclidean Space | Understand the contents covered by the lecture. |
Class 2 | Metric Space and Topological Space | Understand the contents covered by the lecture. |
Class 3 | Basis and Neighborhood System | Understand the contents covered by the lecture. |
Class 4 | Continuous Map | Understand the contents covered by the lecture. |
Class 5 | Induced Topology | Understand the contents covered by the lecture. |
Class 6 | Product Topology | Understand the contents covered by the lecture. |
Class 7 | Hausdorff Space | Understand the contents covered by the lecture. |
Class 8 | Review and Midterm Examination | Confirm your current understanding after reviewing the materials covered by the first half of the course. |
Class 9 | Normal Space and Regular Space | Understand the contents covered by the lecture. |
Class 10 | Separation Axiom and Continuous Map | Understand the contents covered by the lecture. |
Class 11 | Connectivity | Understand the contents covered by the lecture. |
Class 12 | Compactness | Understand the contents covered by the lecture. |
Class 13 | Property of Compact Space | Understand the contents covered by the lecture. |
Class 14 | Completeness of Metric Space | Understand the contents covered by the lecture. |
Class 15 | Completion of Metric Space | Understand the contents covered by the lecture. |
"Set and Topological Space (in Japanese)" by Shigeyuki Morita published by Aasakura Shoten.
Not specified in particular.
By scores of midterm and final examinations. 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.
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.
Toshiaki Murofushi (murofusi[at]c.titech.ac.jp)
To be announced in the first lecture.