Let be the discrete space.

Compute for and for

I know that is defined to be for and for but I don't know exactly how to use that to solve the problem.

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- March 26th 2011, 05:31 PMConnectedDiscrete metric
Let be the discrete space.

Compute for and for

I know that is defined to be for and for but I don't know exactly how to use that to solve the problem. - March 26th 2011, 05:40 PMDrexel28
I assume that is the 'sphere' (that is an uncommon noation) of radius centered at . I think you're overthinking your problem. has a simple formulation. Think about fixing this one point then one can think (purely heuristically) as the situation being analgous to being the origin in and being the unit circle. With this in mind, is the solution clear?

- March 26th 2011, 05:43 PMConnected
No, I don't get it well.

I understand a bit your reasoning, but is there a way to make it analytically?

Thanks for your help. - March 26th 2011, 09:09 PMTinyboss
If , then what happens in the two cases and ? In particular, what do you know if d(x,y)<1 in this metric?