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Locally rich compact sets
- Source :
- Illinois J. Math., Volume 58, Number 3 (2014), 779-806
- Publication Year :
- 2014
-
Abstract
- We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any other compact set of the cube as a tangent at all points or just in a dense sub-set. Here the "almost all compact sets" means that the tangent collection contains a contracted image of any compact set of the cube and that the contraction ratios are uniformly bounded. In the Euclidean space, the distance of sub-sets is measured by the Hausdorff distance. Also the geometric properties and dimensions of such spaces and sets are studied.<br />Comment: 29 pages, 3 figures. Final version
Details
- Database :
- arXiv
- Journal :
- Illinois J. Math., Volume 58, Number 3 (2014), 779-806
- Publication Type :
- Report
- Accession number :
- edsarx.1406.7643
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1215/ijm/1441790390