Generic Properties of Compact Metric Spaces
Metric Geometry
2010-03-29 v1
Abstract
We prove that there is a residual subset of the Gromov-Hausdorff space (i.e. the space of all compact metric spaces up to isometry endowed with the Gromov-Hausdorff distance) whose points enjoy several unexpected properties. In particular, they have zero lower box dimension and infinite upper box dimension.
Cite
@article{arxiv.1003.5087,
title = {Generic Properties of Compact Metric Spaces},
author = {Joël Rouyer},
journal= {arXiv preprint arXiv:1003.5087},
year = {2010}
}