Question

question about simply connected spaces - can't you still apply green's thrm on not simply connected regions, but basically define as many partitions that are balls in the interior of the set that are conservative and then apply greens on each of them? i think topologically it makes sense..

Answer 1

oh, there's no topology in this course. I see. Well, I still think it is sound to use simply connected balls in the interior to apply green's, thus, in the ps8 it is possible to use special care of green's where set is defined everywhere but at the origin, create partitions st\[P_j=\{ x \in|x-a|<\delta \subset R ^{interior} \} \] and go ahead with the Greens.