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i was just wondering if someone (matt) could give me a better idea of what the difference is between the two...thanks
Not quite -- an isomorphism is a homomorphism that has an inverse (that is also a homomorphism).yeah an isomorphism is a homomorphism which is also 1-1 & onto.
i guess those are the analogues in topology... never heard of them explained that way before. i was referring to groups & rings though & yeah i forgot the other operation in the ring. arghHurkyl said:Not quite -- an isomorphism is a homomorphism that has an inverse (that is also a homomorphism).
In some cases, this means exactly what you said. In other cases, it does not. For instance, when discussing topological spaces, the "homomorphisms" are the continuous maps, and "isomorphisms" are the homeomorphic maps. There exist bijective homomorphisms whose inverse is not continuous.
I am sorry to jump in by a very elementary question: is there a way to explain with non-mathematical examples the concept of iso- and homo- morphism? Or to downgrade the level of the mathematical explanation so as to fit brains that are slightly poor in its understanding capabilities for this domain? Thanks so much !Not quite -- an isomorphism is a homomorphism that has an inverse (that is also a homomorphism).
In some cases, this means exactly what you said. In other cases, it does not. For instance, when discussing topological spaces, the "homomorphisms" are the continuous maps, and "isomorphisms" are the homeomorphic maps. There exist bijective homomorphisms whose inverse is not continuous.