THE EXTENSIONS OF C*-ALGEBRAS WITH TRACIAL TOPOLOGICAL RANK NO MORE THAN ONE

Let 0 -> I -> A -> A/I -> 0 be a short exact sequence of C*-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I is TAI (in particular, if A/I is simple and has tracial topological rank no more than one). It will be proved that A has tracial topological rank no more than one if the extension is quasidiagonal, and A has the property (P-1) if the extension is tracially quasidiagonal.