# order topology: What are the limit points of \$ X times mathbb {N} \$?

Leave $$X = {0,1,2 }$$ With topology of natural order and give. $$mathbb {N}$$ Its topology of natural order. To consider $$X times mathbb {N}$$ With the topology of dictionary order.

What are the limit points of $$X times mathbb {N}$$ ?

$$X times mathbb {N} = {(0,1), (0,2), cdots, (0, infty), (1,1), (1,2), cdots, (1, infty), (2,1), (2,2), cdots, (2, infty), cdots }$$