Which sequences converge in the topological space $\left(\mathbb{N}\times\mathbb{N}, \mathcal{J}_{\text{Lexicographic}}\right)$? Which sequences converges in the topological space $\left(\mathbb{N}\times\mathbb{N}, \mathcal{J}_{\text{Lexicographic}}\right)$?
That i have tried:
For each $(p,q)\in \mathbb{N}\times\mathbb{N}$ we have that the sequence $\{(p,q),(p,q),(p,q),\cdots,(p,q)\cdots$} coverges to $(p,q)$ for all $(p,q)\in \mathbb{N}\times\mathbb{N}$.
Am I ok?
Is it correct? Do you have a different example approach? 

ALERT: sorry the next answer is not correct:
I think that you are right.
As we have that $\left(\mathbb{N}\times\mathbb{N}, \mathcal{J}_{\text{Lexicographic}}\right)$ is a discrete space, it has the trivial convergence. By definition, a space $ (X, \mathcal{T})$ has trivial convergence if the only sequences that converges are the constant sequences.
