Resumen
This paper treats the embedding of finite-dimensional subsets of a Banach space into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X - X is finite, dH(X - X) < k, a prevalent set of linear maps from into are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2dB(X). A related argument shows that if the Assouad dimension of X - X is finite and k > dA(X - X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L8(X).