Skip to main content
Have a personal or library account? Click to login
Fundamental Group of n-sphere for n ≥ 2 Cover

Fundamental Group of n-sphere for n ≥ 2

Formalized Mathematics
Volume 20 (2012): Issue 2 (June 2012)
By:  and    
Open Access
|Feb 2013
References

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers., 1():41-46, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The ordinal numbers., 1():91-96, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences., 1():107-114, 1990.
    Search in Google Scholar
  4. [4] Czesław Bylinski. Binary operations., 1():175-180, 1990.
    Search in Google Scholar
  5. [5] Czesław Bylinski. Functions and their basic properties., 1():55-65, 1990.
    Search in Google Scholar
  6. [6] Czesław Bylinski. Functions from a set to a set., 1():153-164, 1990.
    Search in Google Scholar
  7. [7] Czesław Bylinski. Partial functions., 1():357-367, 1990.
    Search in Google Scholar
  8. [8] Czesław Bylinski. Some basic properties of sets., 1():47-53, 1990.
    Search in Google Scholar
  9. [9] Agata Darmochwał. The Euclidean space., 2():599-603, 1991.
    Search in Google Scholar
  10. [10] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts., 2():605-608, 1991.
    Search in Google Scholar
  11. [11] Adam Grabowski. Introduction to the homotopy theory., 6():449-454, 1997.
    Search in Google Scholar
  12. [12] Adam Grabowski and Artur Korniłowicz. Algebraic properties of homotopies., 12():251-260, 2004.
    Search in Google Scholar
  13. [13] Artur Korniłowicz. The fundamental group of convex subspaces ofT., 12():295-299, 2004.
    Search in Google Scholar
  14. [14] Artur Korniłowicz. On the isomorphism of fundamental groups., 12():391-396, 2004.
    Search in Google Scholar
  15. [15] Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls inT., 12():301-306, 2004.
    Search in Google Scholar
  16. [16] Artur Korniłowicz, Yasunari Shidama, and Adam Grabowski. The fundamental group., 12():261-268, 2004.
    Search in Google Scholar
  17. [17] John M. Lee.. Springer-Verlag, New York Berlin Heidelberg, 2000.
    Search in Google Scholar
  18. [18] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions., 1():223-230, 1990.
    Search in Google Scholar
  19. [19] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction., 1():441-444, 1990.
    Search in Google Scholar
  20. [20] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers., 1():777-780, 1990.
    Search in Google Scholar
  21. [21] Marco Riccardi. The definition of topological manifolds., 19():41-44, 2011, doi: 10.2478/v10037-011-0007-4.
    Open DOISearch in Google Scholar
  22. [22] Marco Riccardi. Planes and spheres as topological manifolds. Stereographic projection., 20():41-45, 2012, doi: 10.2478/v10037-012-0006-0.
    Open DOISearch in Google Scholar
  23. [23] Zinaida Trybulec. Properties of subsets., 1():67-71, 1990.
    Search in Google Scholar
  24. [24] Edmund Woronowicz. Relations and their basic properties., 1():73-83, 1990.
    Search in Google Scholar
  25. [25] Edmund Woronowicz. Relations defined on sets., 1():181-186, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-012-0013-1 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 97 - 104
Published on: Feb 2, 2013
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Related subjects:
Computer sciences,
Artificial intelligence,
Computer sciences, other,
Mathematics,
Logic and set theory,
General mathematics

© 2013 Marco Riccardi, Artur Korniłowicz, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 20 (2012): Issue 2 (June 2012)
Next article