Characterizations of conditionally complete partially ordered sets

Pages: 505 - 509, Issue Special, August 2005

 Abstract        Full Text (142.3K)              

Paula Kemp - Department of Mathematics, Missouri State University, Springfield, MO 65897, United States (email)

Abstract: In the mid 1950's Tarski showed that a complete lattice P has the property that every increasing increasing function from P into itself has a fixed point. Anne Davis proved the converse of this result that every lattice with the fixed point property is complete. In this paper, the author proves new equivalences for conditionally complete partially ordered sets with a type of fixed point property. Some comments about these theorems are also given in the paper.

Keywords:  Conditionally Complete, Decreasing, Increasing, and Fixed points.
Mathematics Subject Classification:  Mathematics Subject Classification: Primary 03E25.

Received: October 2004;      Revised: May 2005;      Published: September 2005.