Quotient maps onto submaximal spaces

Asymptotic Geometry of Banach Spaces and Uniform Quotient Maps

Recently, Lima and Randrianarivony pointed out the role of the property (β) of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of (β) of the domain spa...

Relative Compactness and Product Stable Quotient Maps

Hausdorff Dimension of Metric Spaces and Lipschitz Maps onto Cubes

We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than k can be always mapped onto a k-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application we essentially answer a question of Urbański by showing that the transfinite Hausdorff...

ε-weakly Chebyshev subspaces and quotient spaces

Norms on Quotient Spaces