$C\sp{\ast}$-algebra fibre bundles

It will be shown in this paper that for any ${C^\ast}$-algebra fibre bundle with base space $X$ and fibre $A$, a ${C^\ast}$-algebra, the Jacobson spectrum of the ${C^\ast}$-algebra of sections of the fibre bundle can be identified as a topological fibre bundle with the same base space $X$ and fibre the Jacobson spectrum of $A$.