[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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