Real Algebraic and Analytic Geometry

Preprint Server

Previous   Next
140. Andreas Bernig:
Gromov-Hausdorff limits in definable families.


Submission: 2004, October 12.

The notion of piecewise definable metric space is introduced. It is shown that the set of all Gromov-Hausdorff limits of piecewise definable spaces belonging to a fixed bounded definable family is again a definable family. The Gromov-Haudorff limit is taken with respect to the geodesic metric and the word {\it definable} means {\it definable in some o-minimal structure over $\R$.

Mathematics Subject Classification (2000): 14P10, 53C23.

Full text, 10p.: dvi 48k, ps.gz 148k, pdf 210k.

Server Home Page