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2013 | 21 | 2 | 127-131
Tytuł artykułu

Commutativeness of Fundamental Groups of Topological Groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].
Słowa kluczowe
Wydawca
Rocznik
Tom
21
Numer
2
Strony
127-131
Opis fizyczny
Daty
wydano
2013-06-01
Twórcy
  • Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland
Bibliografia
  • [1] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992.
  • [2] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
  • [3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [8] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.
  • [9] Adam Grabowski. Introduction to the homotopy theory. Formalized Mathematics, 6(4): 449-454, 1997.
  • [10] Adam Grabowski and Artur Korniłowicz. Algebraic properties of homotopies. Formalized Mathematics, 12(3):251-260, 2004.
  • [11] Allen Hatcher. Algebraic Topology. Cambridge University Press, 2002.
  • [12] Artur Korniłowicz. The fundamental group of convex subspaces of En T. Formalized Mathematics, 12(3):295-299, 2004.
  • [13] Artur Korniłowicz. The definition and basic properties of topological groups. Formalized Mathematics, 7(2):217-225, 1998.
  • [14] Artur Korniłowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005.
  • [15] Artur Korniłowicz, Yasunari Shidama, and Adam Grabowski. The fundamental group. Formalized Mathematics, 12(3):261-268, 2004.
  • [16] Beata Padlewska. Locally connected spaces. Formalized Mathematics, 2(1):93-96, 1991.
  • [17] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [18] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • [19] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4): 535-545, 1991.
  • [20] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
  • [21] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
  • [22] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • [23] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855-864, 1990.
  • [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_forma-2013-0014
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