## X is a t3 space and A contained in X is an infinite set [closed]

Hi, I need help with a topology problem. The problem is as stated, "Suppose that $X$ is a $T_3$ space and that $A \subset X$ is an infinite set. Show that there are open sets $U_n$ such that $A \cap U_n$ is non-empty for all $n \in \mathbb{N}$ and the closure of any two such $U$'s is empty. In other words these $U$'s are pair wise disjoint.

Now essentially I have started with trying to make my first $U$ and it must be open and contain finitely many points of $A$, but I am having trouble with the wording. I think I just need help getting started, then I should be able to take care of the rest.

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While this is slightly borderline, I think that the context of this question (wanting a hint for an exercise which is known to have a solution) makes it more appropriate for math.stackexchange.com – Yemon Choi Feb 23 2012 at 1:21
Also, as an aside, a worthwhile skill would be to learn to typeset questions such as this (here, or on math.stackexchange.com) using LaTeX. For example, it is much easier to read "... there are open sets $U_n$ such that $A \cap U_n \neq \emptyset$..." – Simon Rose Feb 23 2012 at 4:00