# Calculate interior, closure and boundary

As part of an exercise, I want to calculate the interior, closure and boundary of the following sets in $\mathbb{R}^2$ (with the standard topology).
1. $\mathbb{Z} \times \mathbb{Z}$
2. $\mathbb{Q} \times (\mathbb{Q}\cap]0,+\infty[)$
I found the following solution and would like to verify whether those are correct.
1. Interior: $\emptyset$; Closure: $\mathbb{Z} \times \mathbb{Z}$; Boundary: $\mathbb{Z} \times \mathbb{Z}$
2. Interior: $\emptyset$; Closure: $\mathbb{R} \times (\mathbb{R}\cap[0,+\infty[)$; Boundary: $\mathbb{R} \times (\mathbb{R}\cap[0,+\infty[)$