Have a personal or library account? Click to login
Dilworth's Decomposition Theorem for Posets Cover

Dilworth's Decomposition Theorem for Posets

By: Piotr Rudnicki  
Open Access
|Jul 2010

References

  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  4. [4] Grzegorz Bancerek. Bounds in posets and relational substructures. Formalized Mathematics, 6(1):81-91, 1997.
  5. [5] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Formalized Mathematics, 6(1):93-107, 1997.
  6. [6] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  7. [7] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  8. [8] R. P. Dilworth. A Decomposition Theorem for Partially Ordered Sets. Annals of Mathematics, 51(1):161-166, 1950.10.2307/1969503
  9. [9] P. Erdős and G. Szekeres. A combinatorial problem in geometry. Compositio Mathematica, 2:463-470, 1935.
  10. [10] Adam Grabowski. Auxiliary and approximating relations. Formalized Mathematics, 6(2):179-188, 1997.
  11. [11] L. Mirsky. A Dual of Dilworth's Decomposition Theorem. The American Mathematical Monthly, 78(8).10.2307/2316481
  12. [12] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  13. [13] M. A. Perles. A Proof of Dilworth's Decomposition Theorem for Partially Ordered Sets. Israel Journal of Mathematics, 1:105-107, 1963.10.1007/BF02759805
  14. [14] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
  15. [15] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  16. [16] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.
  17. [17] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
DOI: https://doi.org/10.2478/v10037-009-0028-4 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 223 - 232
Published on: Jul 8, 2010
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2010 Piotr Rudnicki, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 17 (2009): Issue 4 (December 2009)