This is a hard problem in my book ( marked with a star). I don't even see the
question in the problem. I guess it's the last sentence, but I still have no clue to
solve it. Hope someone can gives help.
Suppose is a bounded region. Let be a (two way infinite) line that intersects . Assume that is an interval . Choosing an orientation for , we can define and to be subregions of lying strictly to the left or right of L, with a disjoint union. If a nd are simply connected, then is simply connected.