.4. (a) Let (Xn)nen, (yn)nen be convergent sequences in a metric space (M, d) with limn_oo In = x and limno Yn = y. Show Xn = that d (Xn, Yn) + d(x,y) as n → . [5 points] (b) Determine if a finite metric space is compact. [3 points] (C) Let M1, M2 be metric spaces. Show that a map f: M1 + M2 is continuous if and only if f-1(U) is open in My for any open set U in M2. [5 points] a (d) Show that {(x,y) € R2 : sinergias > 2} is open in R2. () > [5 points]