a) Show that if x Br(a), then there is an > 0 such that the

Question:

a) Show that if x ∈ Br(a), then there is an ∈ > 0 such that the closed ball centered at x of radius ε is a subset of Br{a).
b) If a ≠ b are distinct points in X, prove that there is an r > 0 such that Br(a) ∩ Br(b) = θ.
c) Show that given two balls Br(a) and Bs(b), and a point x ∈ Br(a) ∩ Bs(b), there are radii c and d such that
Bc(x) ⊂ Br(a) ∩ Bs(b) and Bd(x) ⊃ Br(a) U Bs(b).