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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 793848, 9 pages
http://dx.doi.org/10.1155/2011/793848
Research Article

The Bolzano-Poincaré Type Theorems

College of Science, Cardinal Stefan Wyszyński, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa, Poland

Received 24 February 2011; Revised 7 May 2011; Accepted 30 May 2011

Academic Editor: Giuseppe Marino

Copyright © 2011 Przemysław Tkacz and Marian Turzański. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Steinhaus, Kalejdoskop Matematyczny, PWN, Warszawa, Poland, 1954.
  2. H. Steinhaus, Mathematical Snapshot, Oxford University Press, New York, NY, USA, 1969.
  3. W. Surówka, β€œA discrete form of Jordan curve theorem,” Annales Mathematicae Silesianae, no. 7, pp. 57–61, 1993. View at Google Scholar Β· View at Zentralblatt MATH
  4. Y. A. Shaskin, Fixed Points, vol. 2 of Mathematical World, AMS-MSA, 1991.
  5. W. Kulpa, L. Socha, and M. Turzański, β€œSteinhaus chessboard theorem,” Acta Universitatis Carolinae, vol. 41, no. 2, pp. 47–50, 2000. View at Google Scholar Β· View at Zentralblatt MATH
  6. P. Tkacz and M. Turzański, β€œAn n-dimensional version of Steinhaus' chessboard theorem,” Topology and Its Applications, vol. 155, no. 4, pp. 354–361, 2008. View at Publisher Β· View at Google Scholar
  7. H. Poincaré, β€œSur certaines solutions particulieres du probléme des trois corps,” Comptes Rendus de l'Académie des Sciences, vol. 97, pp. 251–252, 1883. View at Google Scholar
  8. H. Poincaré, β€œSur certaines solutions particulieres du probléme des trois corps,” Bulletin Astronomique, vol. 1, pp. 63–74, 1884. View at Google Scholar
  9. C. Miranda, β€œUn' osservazione su una teorema di Brouwer,” Bollettino della Unione Matematica Italiana, p. 527, 1940. View at Google Scholar
  10. W. Kulpa, β€œThe Poincaré-Miranda theorem,” The American Mathematical Monthly, vol. 104, no. 6, pp. 545–550, 1997. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet