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**Deadstar** Is this correct?

Prove that $\displaystyle \overline{A} = X\setminus int(X\setminus A)$

Is it equivalent to prove that $\displaystyle X\setminus\overline{A} = int(X\setminus A)?$

If so then heres my proof...

Let $\displaystyle x \in X$\$\displaystyle \overline{A}$, then $\displaystyle B(x,r) \cap X$\$\displaystyle A = \emptyset$ $\displaystyle \forall r>0$

So then $\displaystyle \exists r > 0$ such that $\displaystyle B(x,r) \subseteq X$\A. Hence $\displaystyle x \in$ int(X\A).

Use [tex]X\setminus A[/tex] to get $\displaystyle X\setminus A$.