- #36

mathwonk

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in fact it is not true that a homeo maps interior to interior. take a homeo from an open disc in the plane to an open disc in R^3, which has no interior. it is still a homeo onto its image but the image has empty interior in R^3. you have to prove that cannot happen when the image is in R^2. it is not at all obvious. well it depends what you mean by obvious. it seems obvious but it is not easy to prove.