(1)[5+10+10分]A function d:M x M → 10,[0,∞) is called an uitrametric if
● d(x, y) = 0 if and only if x = y; ●d(x,y) =d(y,x); ●d(x,z) ≤ max(d(x,y),d(y, z)} for any t,y,z M. We call (M,d) an ultrametric space.
申論題內容
(c) Prove that an ultrametric space must be totally disconnected?.