a1 Department of Mathematics, Faculty of Engineering, Kansai University, Suita, Osaka 564-8680, Japan (email@example.com)
We discuss the three-space problem on discreteness for the Jacobson topology on the spectrum of a C*-algebra in detail. As an application, it is shown that a C*-algebra A is a dual C*-algebra if and only if a closed ideal I of A and the quotient A/I are dual C*-algebras and the open central projection, in the second dual of A, corresponding to I is a multiplier for A.
(Received October 04 1999)
(Accepted May 18 2000)