Let $X=\{0,1,2 \}$ with natural order topology and give $\mathbb{N}$ its natural order topology. Consider $X \times \mathbb{N}$ with the dictionary order topology.
What are the limit points of $X \times \mathbb{N}$ ?
Answer:
$X \times \mathbb{N}=\{(0,1), (0,2), \cdots, (0, \infty), \ (1,1),(1,2), \cdots, (1, \infty), \ (2,1), (2,2), \cdots, (2, \infty) , \cdots \}$
But how to find the limit point?
help me