In this question we consider the standard inclusion of $\mathbb{C}P^{n}\subset \mathbb{C}P^{n+1}$.


It is well known that  $\mathbb{C}P^n$ is  not a retract of  $\mathbb{C}P^{n+1}$.

What about  if  we remove a finite subset as  follows:

**Question:** Assume that $K\subset \mathbb{C}P^n$ is a finite set. Can $\mathbb{C}P^n\setminus K$ be  a  retract of  $\mathbb{C}P^{n+1}\setminus K$?