Functional Equations for Lexicographic Products

Details Functional Equations for Lexicographic Products Functional Equations for Lexicographic Products

2001-07-29

arxiv.org/abs/math/0107206v1

Mathematics

Logic

Scientific paper

We generalize the main result of math.RA/9608214 concerning the convex embeddings of a chain Gamma in a lexicographic power Delta^Gamma. 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 (Delta^Gamma)^{<=0} simeq Gamma, (Delta^Gamma) simeq Gamma, and (Delta^Gamma)^{<0} simeq Gamma.

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