Let J and Je denote the standard topology and the lower-limit topology on R, respectively. Consider the basis B = J X Je for a topology in R2 = R x R and let Jp := (B). (a) Prove that the half-plane {(x, y) E R? | y 2 0} is open with respect to Jp. (b) Prove that the half-plane {(x, y) E R? | x 2 0} is not open with respect to Jp