E = $\{(x,y) \in \mathbb{R}^2 \vert x^2y \geq 0\}$ Border of E?

Question

We use the usual euclidean topology, and I want to find the border of E = $\{(x,y) \in \mathbb{R}^2 \vert x^2y \geq 0\}$ with respect to $\mathbb{R}^2$. I know that the border of E is: Border(E) = Closure(E) $\setminus$ Interior(E). I also know that Border(E) = Closure(E) $\cap$ Closure(X $\setminus$ E).

I try to use the first one, but I'm struggling because I know that this set is closed, but I do not know how to find the interior part of it.

Any hints?

EDIT: Second formula was wrong.

Answer 1

$$\mathring E=\{(x,y)\in\mathbb{R}^2\,|\,x^2y>0\}.$$