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dmuthuk






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Order isomorphism
posted on: 8/13/2007 5:57:58 PM

Hi, I was wondering if the following statement is well defined, and if it is indeed true.

Let X and Y be well ordered sets. If U is a map between X and Y with the property that for each a in X, U bijectively maps the "set of all points strictly smaller than a" to the "set of all points strictly smaller than U(a)", then U is a bijection between X and Y and it preserves order in both directions.
Kanpree




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Order isomorphism
replied on: 9/26/2007 4:55:23 PM

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