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A point on fixpoints in posets

Abstract : Given a non-empty strictly inductive poset X, that is, a non-empty partially ordered set such that every non-empty chain has a least upper bound (a chain being a totally ordered subset), we are interested in sufficient conditions such that, given an element a_0 and a function f:X->X, there is some ordinal k such that a_{k+1}=a_k, where (a_k) is the transfinite sequence of iterates of f starting from a_0. This note summarizes known results about this problem and provides a slight generalization of some of them.
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Preprints, Working Papers, ...
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Contributor : Frédéric Blanqui Connect in order to contact the contributor
Submitted on : Monday, December 22, 2014 - 10:57:46 AM
Last modification on : Friday, January 21, 2022 - 3:15:31 AM
Long-term archiving on: : Monday, March 23, 2015 - 7:11:45 PM


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  • HAL Id : hal-01097809, version 1



Frédéric Blanqui. A point on fixpoints in posets. 2014. ⟨hal-01097809⟩



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