find the closure of A in the co-finite topology

Suppose that $\displaystyle X$ is an infinite set with the co-finite topology, and $\displaystyle A \subseteq X$. Find $\displaystyle Cl(A)$ in the cases where

(a) $\displaystyle A$ finite and (b) $\displaystyle A$ infinite.

I really dont know where to start. Hints would be very useful.

Thanks

Re: find the closure of A in the co-finite topology

Hint: the closed set are the finite subsets of X and X.

Re: find the closure of A in the co-finite topology

Quote:

Originally Posted by

**FGT12** Suppose that $\displaystyle X$ is an infinite set with the co-finite topology, and $\displaystyle A \subseteq X$. Find $\displaystyle Cl(A)$ in the cases where

(a) $\displaystyle A$ finite and (b) $\displaystyle A$ infinite.

Question: What is closure of a closed set?

In part a), is $\displaystyle X\setminus A$ an open set? Why or why not?