3 ms·

By applying the map from I^d to R^d (using the tan-arctan-construction above in each coordinate) after the map from R to R^d, you get a map from R to R^d.

• yarg 3y ago
  I^n is just a countably infinite subset of R^n.
  • Skeime 3y ago
    No, I^n is also uncountable. In fact, the usual proof for the uncountability of R is really proof of the uncountability of I, and then the natural injection into R is used to extend it to R.