Tag: Hausdorff

In this paper we answer a question raised by David H. Fremlin about the Hausdorff measure of R2 with respect to a distance inducing the Euclidean topology. In particular we prove that the Hausdorff n-dimensional measure of Rn is never 0 when considering a distance inducing the Euclidean topology. Fi...

We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov-Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions ...