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2005, 2005(Special): 505-509. doi: 10.3934/proc.2005.2005.505

Characterizations of conditionally complete partially ordered sets

Paula Kemp 1,

1. 

Department of Mathematics, Missouri State University, Springfield, MO 65897, United States

Received  October 2004 Revised  May 2005 Published  September 2005

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: and Fixed points., Increasing, Decreasing, Conditionally Complete.
Mathematics Subject Classification: Mathematics Subject Classification: Primary 03E2.
Citation: Paula Kemp. Characterizations of conditionally complete partially ordered sets. Conference Publications, 2005, 2005 (Special) : 505-509. doi: 10.3934/proc.2005.2005.505
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