Course: Chapters in Topology II

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Course title Chapters in Topology II
Course code MU/03264
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech, English
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • AVERBUCH Vladimír, DrSc.
  • ROTH Samuel Joshua, Mgr. Ph.D.
Course content
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).

Learning activities and teaching methods
Recommended literature
  • D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989.
  • J. L. Kelley. General Topology. Van Nostrand, Princeton, 1957.
  • N. Bourbaki. Topologie générale.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 1 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Summer
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Summer