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? 

$(1,1), (1,2), (1,3), (1,4), (1,5), \ldots$ converges to $(2,1)$.
