Homomorphism vs homeomorphism vs isomorphism

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Homomorphism vs homeomorphism vs isomorphism

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Homomorphism is a mapping between 2 algebraic structures that keeps the operations consistent across the mapping. Examples would be log(x*y) = log(x) + log(y). So this preserves the operations between R to R.

An isomorphism is a mapping whose inverse is also a homomorphism (i.e. a bijective homomorphism). So the operation is preserved perfectly going in the opposite direction.

A homeomorphism is an isomorphism on topologies, specifically.