Fixpoint Theorem for Continuous Functions on Chain-Complete Posets

Kazuhisa Ishida; Yasunari Shidama

Formalized Mathematics (2010)

  • Volume: 18, Issue: 1, page 47-51
  • ISSN: 1426-2630

Abstract

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This text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].

How to cite

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Kazuhisa Ishida, and Yasunari Shidama. "Fixpoint Theorem for Continuous Functions on Chain-Complete Posets." Formalized Mathematics 18.1 (2010): 47-51. <http://eudml.org/doc/266929>.

@article{KazuhisaIshida2010,
abstract = {This text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].},
author = {Kazuhisa Ishida, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {47-51},
title = {Fixpoint Theorem for Continuous Functions on Chain-Complete Posets},
url = {http://eudml.org/doc/266929},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Kazuhisa Ishida
AU - Yasunari Shidama
TI - Fixpoint Theorem for Continuous Functions on Chain-Complete Posets
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 47
EP - 51
AB - This text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].
LA - eng
UR - http://eudml.org/doc/266929
ER -

References

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  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. [2] Grzegorz Bancerek. Bounds in posets and relational substructures. Formalized Mathematics, 6(1):81-91, 1997. 
  3. [3] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996. 
  4. [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  5. [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  6. [6] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  7. [7] Adam Grabowski. On the category of posets. Formalized Mathematics, 5(4):501-505, 1996.[WoS] 
  8. [8] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997. 
  9. [9] Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990. 
  10. [10] Glynn Winskel. The Formal Semantics of Programming Languages. The MIT Press, 1993. 
  11. [11] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  12. [12] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  13. [13] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990. 
  14. [14] Mariusz Żynel and Czesław Byliński. Properties of relational structures, posets, lattices and maps. Formalized Mathematics, 6(1):123-130, 1997. 

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