<正>LetXbeaconnectedfiniteCWcomplexanddx:KO(C(X))→Zbethedimensionfunction.Weshowthat,ifAisaunitalseparablesimplenuclearC*-algebraofTR(A)=0withtheuniquetracialstateandsatisfyingtheUCTsuchthatKO(A)=QkerdxandK1(A)=K1(C(X)).thenAisisomorphictoaninductivelimitofMn!(C(X)).