Let $\tau $ be a topology on set $\mathbb{R} \setminus \mathbb{Q}$ with subset topology from $\mathbb{R}$ (with Euclidean topology).
Find clousure and interior sets:
$A= \lbrace \pi * (1 + \frac{1}{n+1})^{n+1} : n \in \mathbb{N} \rbrace$, $B=\lbrace x \in \mathbb{R} \setminus \mathbb{Q} : 1 < x \le \sqrt2 \rbrace$ , $C= \lbrace e+ \frac{1}{n+1} : n \in \mathbb{N} \rbrace$.
I think that,
$cl(A)=(A \cup \lbrace \pi e \rbrace ) \cap (\mathbb{R} \setminus \mathbb{Q})$,
$int(A)= \emptyset$,
$cl(B)=[1, \sqrt2 ] \cap (\mathbb{R} \setminus \mathbb{Q})$,
$int(B)= \emptyset$,
$cl(C)=(C \cup \lbrace e \rbrace ) \cap (\mathbb{R} \setminus \mathbb{Q})$,
$int(C)= \emptyset$.
Can you tell me, if I think right? If not, I will be grateful for any advice :)