find the closure of A in the co-finite topology

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September 13th 2011, 11:35 AM
FGT12

find the closure of A in the co-finite topology

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

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

Thanks
September 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.
September 13th 2011, 11:55 AM
Plato

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

Quote:

Originally Posted by FGT12

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

Question: What is closure of a closed set?
In part a), is $X\setminus A$ an open set? Why or why not?

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