Does there exist bijective measurable maps between R and Rn?
If so, could you give me an example of that?
Thank you.
Answer
Polish space is a topological space that is isomorphic to a complete separable metric space, for example Rn for any n∈N. For the proof of the following fact, see e.g. here.
Any uncountable Polish space is Borel isomorphic (there exists a bimeasurable bijection) to the space of real numbers R with standard topology.
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