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Physical Sciences and Mathematics Commons

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Applied Mathematics

University of Dayton

1983

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Full-Text Articles in Physical Sciences and Mathematics

The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn Jan 1983

The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Mathematics Faculty Publications

A partially ordered set P is ω-chain complete if every countable chain (including the empty set) in P has a supremum. … Notice that an ω-chain continuous function must preserve order. P has the (least) fixed point property for ω-chain continuous functions if every ω-chain continuous function from P to itself has (least) fixed point.

It has been shown that a partially ordered set does not have to be ω-chain complete to have the least fixed point property for ω-chain continuous functions. This answers a question posed by G. Plotkin in 1978. I.I. Kolodner has shown that an ω-chain complete …