Continous surjective map from $S^1$ to $S^n$ Is there any continous surjective map from $S^1$ or $[0,1]$ onto $S^n$, for some $n\geq 2$. 
Thank you.

Yes, there is. Start with a space filling curve $\gamma \colon [0,1] \to [0,1]^2$. Induction gives you a continuous onto $\gamma_n \colon [0,1] \to [0,1]^{n}$. Identifying the boundary to one point is a quotient map $\pi \colon [0,1]^n \to S^n$, together with $\gamma_n$, we have $\pi \circ\gamma_n \colon [0,1]\to S^n$.
