This is a dumb question, but what's the difference between geometry on discrete sets and homotopy theory on discrete sets, eg, in the spirit of digital topology?
Every set is open, so every set is closed. So something like a closed interval, or the product of closed intervals, is just going to look like the network that defines a line segment, square, etc... right?
In that sense, it seems like the geometry of numbers and the topology of numbers are basically the same thing.
But I'm going to be honest -- I know basically nothing about arithmetic geometry.
Every set is open, so every set is closed. So something like a closed interval, or the product of closed intervals, is just going to look like the network that defines a line segment, square, etc... right?
In that sense, it seems like the geometry of numbers and the topology of numbers are basically the same thing.
But I'm going to be honest -- I know basically nothing about arithmetic geometry.