Let M(n) be the space of real n* n matrices. Regard this as a metric

space with

distance function d(A, B) = sum { i, j = 1 to n } | a_ij - b_ij |

where A = (a_ij) and B = (b_ij). Prove that the subset N subset of M(n)

consisting of

matrices A such that A^k = 0 for some k is a closed subset of M(n).