1) The continuous image of a compact set is compact.
2) Yes. Think about expanding the disk a little, and "capping" the radius of the image at 1.
3) No, but I don't know of a really short proof.
Dear MHF members,
I have the following problem.
Let denote the unit disk in the plane, with interior and boundary .
- Does there exist a continuous surjection ?
- Does there exist a continuous surjection ?
- Does there exist a continuous surjection , which leaves every point on fixed?
Many thanks.
bkarpuz