# find the closure of A in the co-finite topology

• Sep 13th 2011, 11:35 AM
FGT12
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
• Sep 13th 2011, 11:54 AM
girdav
Re: find the closure of A in the co-finite topology
Hint: the closed set are the finite subsets of X and X.
• Sep 13th 2011, 11:55 AM
Plato
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?