M6140 Topology

Faculty of Science
Spring 2002
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Prerequisites (in Czech)
M3100 Mathematical Analysis III
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
Topological spaces: topological spaces, closed sets, closure
Continuous maps: continuous maps, homeomorphisms
Subspaces and products: subspaces, products
Separation axioms: T0 and T1 spaces, Hausdorff spaces, regular spaces, normal spaces
Compact spaces: compact spaces, Tichonov theorem
Connected spaces: connected spaces, components, pathwise connected spaces, locally connected spaces, continuum, Cantor discontinuum
Homotopy: homotopy, simply connected spaces, fundamental group, applications of a fundamental group
Real functions: completely regular spaces, Urysohn lemma, Tietze theorem
Locally compact spaces: locally compact spaces, one-point compactification
Brouwer fix point theorem: complexes, triangulation, Sperner lemma, Brouwer theorem
Literature
  • PULTR, Aleš. Podprostory euklidovských prostorů. Vyd. 1. Praha: SNTL - Státní nakladatelství technické literatury, 1986, 253 s. info
  • CHVALINA, Jan. Obecná topologie. Vyd. 1. Brno: Univerzita J.E. Purkyně, 1984, 193 s. info
  • PULTR, Aleš. Úvod do topologie a geometrie. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 231 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Spring 2002, recent)
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