Monday, 6 May 2013

order theory - langlemathbbRtimesmathbbR,letextlexrangle and langlemathbbRtimesmathbbQ,letextlexrangle are not isomorphic

Prove that ordered sets R×R,lex and R×Q,lex are not isomorphic (lex means lexicographical order).



I know that to prove that ordered sets are isomorphic, I would make a monotonic bijection, but how to prove they aren't isomorphic?

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