[FOM] metrics

Adam Epstein adame at maths.warwick.ac.uk
Wed Feb 2 04:45:34 EST 2005

>One point where I got lost was Definition 7.3, the definition of Al(M).
>I don't understand the definition:

>   Define Al(M) to be the subset of Met(M) consisting of the
>   closure in the Gromov-Hausdorff metric of isometry classes
>   of metrics (in Riem(M)/Diff(M).

> Isn't everything in Met(M) an isometry class of a metric?

Met(M) consists of isometry classes of metrics. These are not necessarily
Riemannian metrics, so passing to the Gromov-Haudorff closure represents
nontrivial operation.

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