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Mathematics Forum
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| Author | Message / Information |
| dmuthuk Quote | Reply | | 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. |
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Kanpree
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Order isomorphism
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