  One shows that for two C^*-algebras A_1 and A_2 any continuous function on
Prim(A_1)\times Prim(A_2) can be continuously extended to Prim(A_1\otimes A_2)
provided it takes its values in a T_1 topological space. This generalizes a
1977 result of L.G. Brown. A new proof is given for a result of R.J. Archbold
about the space of minimal primal ideals of A_1\otimes A_2. To obtain these two
results one makes use of the topological properties of the space of prime
ideals of the minimal tensor product.
