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} $ ?

**Reply:**

$ 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 } $

But how to find the limit point?

help me