jem05
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Hello,
I know the hyperreals are not connected with respect to the interval opens (open sets are open intervals) In fact *R is totally disconnected.
Is *R connected with respect to the S-open topology (open ball around x of radius r is ((x-r, x+r)) any point in this set has its halo in the set also. In other words, you take the interval (x-r, x+r) and take out the points of infinitessimal distance with the endpoints. You are then left with ((x-r, x+r)).
If *R is not connected, what are the connected components?
Thank you
I know the hyperreals are not connected with respect to the interval opens (open sets are open intervals) In fact *R is totally disconnected.
Is *R connected with respect to the S-open topology (open ball around x of radius r is ((x-r, x+r)) any point in this set has its halo in the set also. In other words, you take the interval (x-r, x+r) and take out the points of infinitessimal distance with the endpoints. You are then left with ((x-r, x+r)).
If *R is not connected, what are the connected components?
Thank you