MU03263 Chapters in Topology I

Mathematical Institute in Opava
Winter 2017
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
Vladimír Averbuch, DrSc. (lecturer)
Mgr. Samuel Joshua Roth, Ph.D. (seminar tutor)
Guaranteed by
Vladimír Averbuch, DrSc.
Mathematical Institute in Opava
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
Course objectives
Repetition and deepening of some chapters of usual course of topology. Some further chapters.
Syllabus
  • 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).
Literature
    recommended literature
  • N. Bourbaki. Topologie générale. info
  • D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989. info
  • J. L. Kelley. General Topology. Van Nostrand, Princeton, 1957. info
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2017, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2017/MU03263