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A Theorem on Partially Ordered Sets and its Application

Published online by Cambridge University Press:  09 April 2009

Vladimir Devidé
Vladimir Devidé
Affiliation:
Institute of Mathematics University of Zagreb, Yugoslavia
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Let (S, ≦) be a (non-void) partially ordered set with the property that for every (non-void) chain C (i.e., every totally ordered subset) of S, there exists in S the element sup C. Let SM be the set of all maximal elements s of S. ƒ:S/SM→S be a slowly increasing mapping in the sense that

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 361 - 362
Copyright
Copyright © Australian Mathematical Society 1969