Memoirs of the American Mathematical Society 1995; 89 pp; softcover Volume: 115 ISBN10: 0821826115 ISBN13: 9780821826119 List Price: US$41 Individual Members: US$24.60 Institutional Members: US$32.80 Order Code: MEMO/115/550
 This work shows that the Weylvon Neumann theorem for unitaries holds for \(\sigma\)unital \(AF\)algebras and their multiplier algebras. Lin studies \(E(X,A)\), the quotient of \(\mathrm{{\mathbf{Ext}}}^{eu}_s(C(X),A)\) by a special class of trivial extension, dubbed totally trivial extensions. This leads to a BDFtype classification for extensions of \(C(X)\) by a \(\sigma\)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 Weylvon NeumannBerg theorem. Readership Research mathematicians. Table of Contents  Introduction
 Totally trivial extensions
 The functor \(E(\cdot \,, A)\)
 BDF theory for \(C^*\)algebras with real rank zero
 Extensions by finite matroid algebras
 References
