MU:MU03264 Chapters in Topology II - Course Information
MU03264 Chapters in Topology II
Mathematical Institute in OpavaSummer 2013
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Vladimír Averbuch, DrSc. (lecturer)
doc. RNDr. Zdeněk Kočan, Ph.D. (seminar tutor) - Guaranteed by
- Vladimír Averbuch, DrSc.
Mathematical Institute in Opava - Prerequisites (in Czech)
- MU03252 Chapters in Topology I || MU03263 Chapters in Topology I
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Geometry and Global Analysis (programme MU, N1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematical Analysis (programme MU, N1101)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Secondary School Teacher Training in Mathematics (programme FPF, M7504)
- Course objectives
- Repetition and deepening of some chapters of usual course of topology. Some further chapters.
- Syllabus
- 1. Uniform spaces (multi-valued functions, entourages, induced topology, uniform continuity).
2. Complete spaces and completion (Cauchy filters, minimal Cauchy filters, completeness, theorem on completion, completeness and completion of subspaces and products).
3. Compactness and uniform structure (uniformity of compact spaces, pre-compactness, compactness of uniform spaces, compact sets in uniform spades).
4. Stone-Čech theorem (evaluation mapping, compactification, Stone-Čech theorem).
5. Ascoli theorem (uniform convergence, equi-continuity, Ascoli theorem).
- 1. Uniform spaces (multi-valued functions, entourages, induced topology, uniform continuity).
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2013, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2013/MU03264