DearMHFmembers,

I have the following problem.

Let $\displaystyle \mathbb{D}:=\{(x,y):\ x^{2}+y^{2}\leq1\}$ denote the unit disk in the plane, with interior $\displaystyle \mathbb{D}^{\circ}$ and boundary $\displaystyle \partial\mathbb{D}$.

- Does there exist a continuous surjection $\displaystyle f:\mathbb{D}\to\mathbb{D}^{\circ}$?
- Does there exist a continuous surjection $\displaystyle f:\mathbb{D}^{\circ}\to\mathbb{D}$?
- Does there exist a continuous surjection $\displaystyle h:\mathbb{D}\to\partial\mathbb{D}$, which leaves every point on $\displaystyle \partial\mathbb{D}$ fixed?

Many thanks.

bkarpuz