Let $X = \{0,1,2,3,\ldots\}$ (the non-negative integers), let $$B_1 = \{\{n\} : n \in X \text{ and }n > 0\}= \{\{1\}, \{2\}, \{3\},\ldots\}$$ $$B_2 = \{Z \subset X : X \setminus Z = \{1,2,\ldots n\} \text{ for some }n \in \mathbb{N} \}$$
a) Prove that $B$ is a basis for a topology on $X$.
b) Let $T$ be the topology from part 1. Prove that $(X; T )$ is $T_2$.