Commutativeness of Fundamental Groups of Topological Groups

Artur Korniłowicz

Formalized Mathematics (2013)

  • Volume: 21, Issue: 2, page 127-131
  • ISSN: 1426-2630

Abstract

top
In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].

How to cite

top

Artur 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. [1] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992. 
  2. [2] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990. 
  3. [3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  4. [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. 
  5. [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  6. [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  7. [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  8. [8] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991. 
  9. [9] Adam Grabowski. Introduction to the homotopy theory. Formalized Mathematics, 6(4): 449-454, 1997. 
  10. [10] Adam Grabowski and Artur Korniłowicz. Algebraic properties of homotopies. Formalized Mathematics, 12(3):251-260, 2004. 
  11. [11] Allen Hatcher. Algebraic Topology. Cambridge University Press, 2002. Zbl1044.55001
  12. [12] Artur Korniłowicz. The fundamental group of convex subspaces of En T. Formalized Mathematics, 12(3):295-299, 2004. 
  13. [13] Artur Korniłowicz. The definition and basic properties of topological groups. Formalized Mathematics, 7(2):217-225, 1998. 
  14. [14] Artur Korniłowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005. 
  15. [15] Artur Korniłowicz, Yasunari Shidama, and Adam Grabowski. The fundamental group. Formalized Mathematics, 12(3):261-268, 2004. 
  16. [16] Beata Padlewska. Locally connected spaces. Formalized Mathematics, 2(1):93-96, 1991. 
  17. [17] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  18. [18] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  19. [19] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4): 535-545, 1991. 
  20. [20] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990. 
  21. [21] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003. 
  22. [22] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  23. [23] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855-864, 1990. 
  24. [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  25. [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. 
  26. [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.