n ek) k=1 ek is = k+1 k 0 n-> ktoo ktoo no 3: (a) For each n e Zt, let Xn = (In,k)k>1 E R be given by In kule where the kith standard basis vector in R (so we have Xn,k when k n). Find lim ( lim In,k) in R, and find lim ( lim In,k) in R, and determine whether the sequence (2n)n>1 converges in (loo, doo). (b) Let A denote the set of all sequences a = (an)n>1 E ly for which lan| 5 2h for all ne Z+. Show that the interior of A is empty in (li,d). (c) Let I : R + R be the identity map given by I(x) = x for all x E R. Determine whether I is continuous as a map I :(R, di) (R, d2) and whether I is continuous as a map I : (R, d2) + (R, d). n ek) k=1 ek is = k+1 k 0 n-> ktoo ktoo no 3: (a) For each n e Zt, let Xn = (In,k)k>1 E R be given by In kule where the kith standard basis vector in R (so we have Xn,k when k n). Find lim ( lim In,k) in R, and find lim ( lim In,k) in R, and determine whether the sequence (2n)n>1 converges in (loo, doo). (b) Let A denote the set of all sequences a = (an)n>1 E ly for which lan| 5 2h for all ne Z+. Show that the interior of A is empty in (li,d). (c) Let I : R + R be the identity map given by I(x) = x for all x E R. Determine whether I is continuous as a map I :(R, di) (R, d2) and whether I is continuous as a map I : (R, d2) + (R, d)