It is well known that there does NOT exist a homeomorphism between R^m and R^n if m>n. My question is whether it is possible to construct a homeomorphism between R^m (as a whole) and a subset of R^n (note that we also suppose that m>n)?(adsbygoogle = window.adsbygoogle || []).push({});

Intuitively, it is impossible. Is my intuition right? Thank you for your replying in advance!

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# A fundamental question on homeomorphism

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