Hausdorff dimension of metric spaces and Lipschitz maps onto cubes

Details Hausdorff dimension of metric spaces and Lipschitz maps onto cubes Hausdorff dimension of metric spaces and Lipschitz maps onto cubes

2012-03-03

arxiv.org/abs/1203.0686v1

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

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 Urba\'nski by showing that the transfinite Hausdorff dimension (introduced by him) of an analytic subset $A$ of a complete separable metric space is the integer part of $\dim_H A$ if $\dim_H A$ is finite but not an integer, $\dim_H A$ or $\dim_H A-1$ if $\dim_H A$ is an integer and at least $\omega_0$ if $\dim_H A=\infty$.

Affiliated with

Also associated with

No associations

Rating

Hausdorff dimension of metric spaces and Lipschitz maps onto cubes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hausdorff dimension of metric spaces and Lipschitz maps onto cubes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hausdorff dimension of metric spaces and Lipschitz maps onto cubes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331189