Someone called Bob told me:
Definition of closure: $\overline{A}=\{x_0: \forall \epsilon>0, > (x_0-\epsilon,x_0+\epsilon) \cap A =\emptyset\}$
From https://math.stackexchange.com/posts/1776563/edit
They said:
Let $A\subseteq\mathbb{C}$ be given. The closure of A is $\overline{A}=\left\{z:\forall\epsilon>0, > D_{\epsilon}\left(z\right)\cap A\neq\phi\right\}$
Royden said
$x$ is a point of closure of $E$ if every open interval containing $x$ also contains a point of $E$.
My interpretation is that Bob is wrong according to Royden and the link.
therefore Bob should have defined it as $\bar{A}=\{x_0: \forall \epsilon>0, (x_0-\epsilon,x_0+\epsilon) \cap A \neq \emptyset\}$?
Who is right? What is closure?