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Thread: Special Property?

  1. #1
    Senior Member Sampras's Avatar
    May 2009

    Special Property?

    Is there any name given to this: Suppose  \langle S, * \rangle ,  \langle S', *' \rangle and  \langle S'', *'' \rangle are binary structures. Suppose there is an isomorphism  \phi between  S and  S' . Also suppose  S and  S' are isomorphic. Also  S' and  S'' are isomorphic, and the same isomorphism  \phi are used.
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  2. #2
    MHF Contributor Matt Westwood's Avatar
    Jul 2008
    Reading, UK
    By definition, an isomorphism is a function.

    Two functions are identical only if the domains and ranges are the same.

    So unless S = S' = S'' it's not possible for the same isomorphism to be used for \phi: S \to S' as it is for \phi: S' \to S'' because by definition the two isomorphism would need to be different.

    As to whether there's a name for this or not, I haven't a clue, but unless there are some unspoken assumptions (or it's a trick question), I'd question what's going on here.
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