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Calabi-Yau Mirror symmetry can be regarded as T-duality on a three-dimensional torus. Starting with a 3-torus equipped with H-flux and possibly with D0-branes, T-duality transformations will eventually lead to a non-geometric torus with R-flux and D3-branes. As we will discuss this non-geometric background possesses for closed and for open strings an interesting non-associative geometric structure.