Darren New wrote:
> Now define "distance".

I thought the underlying assumption in this thread was that we're 
dealing spaces equipped with a metric tensor, do you automatically get a 
definition of distance in the standard manner.  How does this require 
extra care to define?

I suppose you could argue that circles are a bit trickier to define, but 
I think the normal one will work well, and should even be well-behaved 
on genus-0 manifolds, or locally on any smooth manifold (like spherical 
or hyperbolic spaces).

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