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Annulus : X and Y cannot be Homomorphic

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24. Let X,Y be the subspace of the plane shown as below. Under the assumption that any homomorphism from the annulus to itself must send the points of the two boundary circles among themselves, argue that X and Y cannot be homomorphic.

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Homomorphism in an annulus is investigated. The solution is detailed and well presented.

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Suppose that there exist a homeomorphism between X and Y.
Let A, B, a, b be the points ...

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