How can I prove that every subset of R^n is homeomorphic to a closed subset of R^(n+1)? Does this only works for real number only as R is metrizable?
Thanks.
Isn't that what we're doing? We want a homeomorphism of $\displaystyle \mathbb{R}^n$ into some subset of $\displaystyle \mathbb{R}^{n+1}$. In this case, we implicitly chose the subset $\displaystyle \{(x_1,\ldots,x_n,0)\in \mathbb{R}^{n+1}\ |\ x_1,\ldots,x_n\in \mathbb{R}\}$.