For each $\displaystyle n\in Z_+$, let $\displaystyle B_n = {n, n+1, n+2, ....}$ and consider the collectionB= $\displaystyle {B_n | n\in Z_+}$

(a) Show thatBis a basis for a topology for $\displaystyle Z^+$

(b) Show thte the topology on X generated byBis not Hausdorff

(c) Show that the sequence (2,4,6,8,...) converges to every point in $\displaystyle Z_+$ with the topology generated byB