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Let X be any topological space, and let A,B be subspaces of X that are homeomorphic

to each other. Does it follow that the quotients X/A and X/B are homeomorphic?

I know this is true if A,B are both contractible in X , since we then have X/A ~X ~X/B

But I'm not sure otherwise. Any ideas?

Thanks in Advance.

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# Are Quotients by Homeomorphic Subspaces Homeomorphic?

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