Continuous map $\mathbb{S}^n\to \mathbb{S}^m$
Is it true that any continuous map $\mathbb{S}^n\to \mathbb{S}^m$ is not surjective if $n<m$?
Thanks.
Solution 1:
No, it is not true. There are variations of the Peano curve which provide surjective maps $S^1\to S^n$ for all $n\geq1$.