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I'd like a confirm about this little exercise.

Let $X=${$1,2,3,4,5,6$} and $\tau=${$\emptyset,X$,{$1,2$} , {$1,2,5$} , {$1,2,6$} , {$1,2,5,6$}}. Let $E=${$1,2,3$}. Find closure, interior and boundary.

I got that the interior is $Int(E)=$ {1,2}, because it's the biggest open set contained in $E$.

For the closure: al the closed sets don't contain $1$ and $2$, so the smallest closed set that contains $E$ is $X$: $Cl(E)=X$.

The boundary $\partial E=Cl(E) \setminus Int(E)=X\setminus${1,2} $ = ${3,4,5,6}.

Is it okay?

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    $\begingroup$ Yes, it is correct! $\endgroup$ – Onil90 Aug 17 '17 at 11:40
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    $\begingroup$ For the closure of $E$ you should say that $X$ \ $\overline E $ is an open set not containing $1,$ so $X$ \ $\overline E$ is empty, so $\overline E=X.$.... This is, I think, what you meant. It's a little hard to state it right. Your work is correct. $\endgroup$ – DanielWainfleet Aug 18 '17 at 4:05

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