Hi, I'm having trouble with this:
Prove that the set R2\ Q2 is connected
Recall that .
So suppose that .
Construct a polygonal path from which is a subset of .
There are several cases. I will help with one.
If there is a linear path from : .
And there is a linear path from : .
Putting the two together we have a polygonal path from which is a subset of .
There are other cases. But in each you can show pathwise connectivity.