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I have this formula, $A=\operatorname{int}(A)\cup \delta(A)$. It says that a set is equal to its interior union its boundary. What goes wrong here: $A=$ the rationals on the real line. Then $\operatorname{int}(A)=\{\}$. Boundary of $A$ is $\mathbb{R}$, so $A=\mathbb{R}$, but $A$ is not $\mathbb{R}$?

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    Seems like a typo yes, i think I get this now, thanks. close topic2011-12-31

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Your formula should be $\overline{A} = \operatorname{Int(A)} \cup \operatorname{Bd}(A)$ for subsets $A$ of a topological space $X$. And for $\mathbb{Q}$ the closure equals the boundary, namely $\mathbb{R}$, so no problem there....