Generic Properties of Compact Metric Spaces

Details Generic Properties of Compact Metric Spaces Generic Properties of Compact Metric Spaces

2010-03-26

arxiv.org/abs/1003.5087v1

Mathematics

Metric Geometry

Scientific paper

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.

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