$C^*$-Algebra Extensions Of $C(X)$

This work shows that the Weyl-von Neumann theorem for unitaries holds for *s-unital AF-algebras and their multiplier algebras. Lin studies E(X,A), the quotient of Ext[s]eu(C(X),A) by a special class of trivial extension, dubbed totally trivial extensions. This leads to a BDF-type classification for extensions of C(X) by a *s-unital purely infinite simple C] *-algebra with trivial K[1-group. Lin also shows that, when X is a compact subset of the plane, every extension of C(X) by a finite matroid C]*-algebra is totally trivial. Classification of these extensions for nice spaces is given, as are some other versions of the Weyl-von Neumann-Berg theorem.