MU03264 Chapters in Topology II

Mathematical Institute in Opava
Summer 2011
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
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).
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
Czech
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 Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020.
  • Enrolment Statistics (Summer 2011, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2011/MU03264