Commutativeness of Fundamental Groups of Topological Groups
Formalized Mathematics (2013)
- Volume: 21, Issue: 2, page 127-131
- ISSN: 1426-2630
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topArtur Korniłowicz. "Commutativeness of Fundamental Groups of Topological Groups." Formalized Mathematics 21.2 (2013): 127-131. <http://eudml.org/doc/267504>.
@article{ArturKorniłowicz2013,
abstract = {In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].},
author = {Artur Korniłowicz},
journal = {Formalized Mathematics},
keywords = {fundamental group; topological group},
language = {eng},
number = {2},
pages = {127-131},
title = {Commutativeness of Fundamental Groups of Topological Groups},
url = {http://eudml.org/doc/267504},
volume = {21},
year = {2013},
}
TY - JOUR
AU - Artur Korniłowicz
TI - Commutativeness of Fundamental Groups of Topological Groups
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 2
SP - 127
EP - 131
AB - In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].
LA - eng
KW - fundamental group; topological group
UR - http://eudml.org/doc/267504
ER -
References
top- [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. Zbl1044.55001
- [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.
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