(v) [[[int(Q, E)].sup.c] = [[union] {(K, E) : (K, E) [subset or equal to] (Q, E) and (K, E) is NCSOS in X}].sup.c] = [intersection] {[(K, E).sup.c] : [(Q, E).sup.c] [subset or equal to] [(k, E).sup.c] and [(K, E).sup.c] is NCSCS in X}]} = cl[[(Q, E).sup.c]].

(vi) [[[cl(Q, E)].sup.c] = [[intersection] {(K,E) : (K,E) [subset or equal to] (Q,E) and (K,E) is NCSCS in X}].sup.c] = [[union] {[(K, E).sup.c] : [(K, E).sup.c] [subset or equal to] [(Q, E).sup.c] and [(K, E).sup.c] is NCSOS in X}].sup.c]} = int[[(Q,E).sup.c]]..

Since B is a (NCSOS), we have B [subset or equal to] cl(int(B)).

A subset A of X is NC[alpha]OS if and only if it is NCPOS and NCSOS,

sNCint(A) = [union] {G : G is a NCSOS in X and G [subset or equal to] A},

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