# Question on CP^n.

Gold Member
I am asked to construct an onto and continuous function from $$D^{2n}$$ onto $$\mathbb{C}P^n$$ such that it's one- to -one on the interior of $$D^{2n}$$.

I was thinking of sending the line that joins two antipodal points on the boundary of this ball, is this right, or should I be looking for something else?

Thanks.

## Answers and Replies

lavinia
Gold Member
I am asked to construct an onto and continuous function from $$D^{2n}$$ onto $$\mathbb{C}P^n$$ such that it's one- to -one on the interior of $$D^{2n}$$.

I was thinking of sending the line that joins two antipodal points on the boundary of this ball, is this right, or should I be looking for something else?

Thanks.

For the 2 sphere - CP1 - just map the boundary of the disk to the south pole. Generalize this.

Gold Member
I don't understand how does this maps D^2n onto CP^n?

Gold Member
I mean CP^n is homeomorphic to a sphere of S^{2n+1}, so if I map S^2n to a point at the south pole of S^2n, I don't see how does this mapping cover all of S^{2n+1} ~ CP^n?

quasar987