In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].
@article{bwmeta1.element.doi-10_2478_forma-2013-0014, author = {Artur Korni\l owicz}, title = {Commutativeness of Fundamental Groups of Topological Groups}, journal = {Formalized Mathematics}, volume = {21}, year = {2013}, pages = {127-131}, zbl = {1298.55008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0014} }
Artur Korniłowicz. Commutativeness of Fundamental Groups of Topological Groups. Formalized Mathematics, Tome 21 (2013) pp. 127-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0014/
[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. | Zbl 1044.55001
[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.