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Homework Statement
Prove that R and R^2 are not homeomorphic.
The Attempt at a Solution
So, to prove this, one needs to conclude that there is no homeomorphism between R and R^2. A homeomorphism is a continuous bijection f with a continuous inverse. (Does there exist a bijection at all between these two sets? I assume yes, since they have the same cardinality, but I don't see how to construct it.)
Assume such mapping f exists - could we derive a contradiction here. I'm really clueless.