Abstract
LetP, Q be ordered sets and leta∈P. IfP \ {a} is a retract ofP and setsP and {x∈P:x>p} (or its dual) have the fixed point property then, for each chain complete setP,P×Q has the fixed point property if and only if (P\{a})×Q has this property. This establishes the fixed point property for some products of ordered sets which are beyond the reach of all known product theorems.
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Communicated by I. Rival
The work of the first of authors was supported in part by the K.B.N. Grant No. 2 2037 92 03.
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Rutkowski, A., Schröder, B.S.W. Retractability and the fixed point property for products. Order 11, 353–359 (1994). https://doi.org/10.1007/BF01108767
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DOI: https://doi.org/10.1007/BF01108767