  We extend the $C^{\ast}-$algebraic formalism of Topological T-duality to
section algebras of locally trivial bundles of strongly self-absorbing
$C^{\ast}-$algebras and to a larger class of String Theoretic dualities. We
argue that physically this corresponds extending Topological T-duality to Flux
Backgrounds of Type II String Theory which possess topologically nontrivial
sourceless Ramond-Ramond flux. We demonstrate a map in $K-$theory for the
$C^{\ast}-$algebras involved in both sides of this generalized duality. We
calculate a few examples. We discuss the physical relevance of the above
formalism in some detail, in particular, we argue that the above formalism
models String Theoretic tree-level dualities found in such Flux Backgrounds
such as Fermionic T-duality and Timelike T-duality.
