The construction used in the Dauns-Hofmann theorem defines a Banach bundle $\pi:X\to M$ that corresponds to any $C^*$-subalgebra $A$ lying in the center of a $C^*$-algebra $B$ (this is described for example in the monography by M.Dupre and R.Gillette, "Banach bundles, Banach modules and automorphisms of C*-algebras"). This construction can be easily generalized to topological modules over commutative involutive topological algebras (the Dauns-Hofmann theorem need not to be valid, of course, in this general case).
I wonder if the total space $X$ in this bundle $\pi:X\to M$ (at least in the case of $C^*$-algebras) possesses a natural uniform structure (that defines its topology)?
