Functional Equations for Lexicographic Products
Abstract
We generalize the main result of math.RA/9608214 concerning the convex embeddings of a chain Gamma in a lexicographic power DeltaGamma. For a fixed nonempty chain Delta, we derive necessary and sufficient conditions for the existence of nonempty solutions Gamma to each of the lexicographic functional equations (DeltaGamma)<=0 simeq Gamma, (DeltaGamma) simeq Gamma, and (DeltaGamma)<0 simeq Gamma.
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