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Brouwer Fixed Point Theorem for Simplexes Cover

Brouwer Fixed Point Theorem for Simplexes

Formalized Mathematics
Volume 19 (2011): Issue 3 (September 2011)
By: Karol Pąk  
Open Access
|Apr 2012

References

  1. Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
    Search in Google Scholar
  2. Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  3. Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  4. Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  5. Grzegorz Bancerek and Yasunari Shidama. Introduction to matroids. Formalized Mathematics, 16(4):325-332, 2008, doi:10.2478/v10037-008-0040-0.10.2478/v10037-008-0040-0
    Search in Google Scholar
  6. Leszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991.
    Search in Google Scholar
  7. Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
    Search in Google Scholar
  8. Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
    Search in Google Scholar
  9. Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  10. Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  11. Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.
    Search in Google Scholar
  12. Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990.
    Search in Google Scholar
  13. Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
    Search in Google Scholar
  14. Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
    Search in Google Scholar
  15. Alicia de la Cruz. Totally bounded metric spaces. Formalized Mathematics, 2(4):559-562, 1991.
    Search in Google Scholar
  16. Roman Duda. Wprowadzenie do topologii. PWN, 1986.
    Search in Google Scholar
  17. Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003.
    Search in Google Scholar
  18. Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
    Search in Google Scholar
  19. Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.
    Search in Google Scholar
  20. Artur Korniłowicz. The correspondence between n-dimensional Euclidean space and the product of n real lines. Formalized Mathematics, 18(1):81-85, 2010, doi: 10.2478/v10037-010-0011-0.10.2478/v10037-010-0011-0
    Search in Google Scholar
  21. Yatsuka Nakamura, Andrzej Trybulec, and Czesław Byliński. Bounded domains and unbounded domains. Formalized Mathematics, 8(1):1-13, 1999.
    Search in Google Scholar
  22. Adam Naumowicz. On Segre's product of partial line spaces. Formalized Mathematics, 9(2):383-390, 2001.
    Search in Google Scholar
  23. Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
    Search in Google Scholar
  24. Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
    Search in Google Scholar
  25. Karol Pąk. Small inductive dimension of topological spaces. Formalized Mathematics, 17(3):207-212, 2009, doi: 10.2478/v10037-009-0025-7.10.2478/v10037-009-0025-7
    Search in Google Scholar
  26. Karol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.10.2478/v10037-010-0012-z
    Search in Google Scholar
  27. Karol Pąk. Abstract simplicial complexes. Formalized Mathematics, 18(1):95-106, 2010, doi: 10.2478/v10037-010-0013-y.10.2478/v10037-010-0013-y
    Search in Google Scholar
  28. Karol Pąk. Sperner's lemma. Formalized Mathematics, 18(4):189-196, 2010, doi: 10.2478/v10037-010-0022-x.10.2478/v10037-010-0022-x
    Search in Google Scholar
  29. Karol Pąk. Continuity of barycentric coordinates in Euclidean topological spaces. Formalized Mathematics, 19(3):139-144, 2011, doi: 10.2478/v10037-011-0022-5.10.2478/v10037-011-0022-5
    Search in Google Scholar
  30. Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
    Search in Google Scholar
  31. Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.
    Search in Google Scholar
  32. Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
    Search in Google Scholar
  33. Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
    Search in Google Scholar
  34. Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  35. Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-011-0023-4 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 145 - 150
Published on: Apr 26, 2012
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Mathematics,
General mathematics,
Computer sciences,
Computer sciences, other

© 2012 Karol Pąk, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 19 (2011): Issue 3 (September 2011)