topology on $\mathbb{Q}\times \mathbb{Q}$

Question

on $\mathbb{Q}\times \mathbb{Q}$ we define a bases of open sets for each $(x,x')\in \mathbb{Q}\times \mathbb{Q}$ by

$$ \mathcal{B}_{x,x'}=\{(z,y)\in \mathbb{Q}\times \mathbb{Q}: \, x<z<x', y\in \mathbb{Q}\}$$

the question is to find $cl(A)$ and $int(A)$ where $$A=\{(x,y)\in \mathbb{Q}\times \mathbb{Q}: x^2+y^2=1\}$$

I don't know how to get it, I don't understand the topology.

Answer 1

The base is vertical strips of the plane without the edges.
int A is empty, cl A = [-1,1]×Q.

The open sets are U×Q where U is open within Q.
The closed sets are K×Q where K is closed within Q.