Fixed points and complete lattices
Abstract
Tarski proved in 1955 that every complete lattice has the fixed point property. Later, Davis proved the converse that every lattice with the fixed point property is complete. For a chain complete ordered set, there is the well known Abian-Brown fixed point result. As a consequence of the Abian-Brown result, every chain complete ordered set with a smallest element has the fixed point property. In this paper, a new characterization of a complete lattice is given. Also, fixed point theorems are given for decreasing functions where the partially ordered set need not be dense as is the usual case for fixed point results for decreasing functions.
Department(s)
Mathematics
Document Type
Conference Proceeding
DOI
https://doi.org/10.3934/proc.2007.2007.568
Keywords
Complete lattices, Decreasing, Fixed points, Increasing
Publication Date
9-1-2007
Recommended Citation
Kemp, Paula. "Fixed Points and Complete Lattices." In Conference Publications, vol. 2007, no. Special, p. 568. American Institute of Mathematical Sciences, 2007.
Journal Title
Discrete and Continuous Dynamical Systems- Series A
