Course: Chapters in Topology I

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Course title Chapters in Topology I
Course code MU/03263
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
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
Lecturer(s)
  • AVERBUCH Vladimír, DrSc.
  • ROTH Samuel Joshua, Mgr. Ph.D.
Course content
1. Filters (filter basis, trace of a filter, operations over filters, ultrafilters and their basic properties). 2. Filters and topologies (convergent filters, description of topologinal notions in terms of filters). 3. Separability (separability axioms, equivalent characterizations of Hausdorff separability, theorem on continuous extension). 4. Initial topology (definition and basic examples, description of initial topology in terms of filters, subspaces and products). 5. Compactness (equevalent characterizations of compactness, Tichonov Theorem).

Learning activities and teaching methods
unspecified
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 Winter
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Winter
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Winter