Re: Help on a proof related to the boundary of a star-shaped set

["Yajun Wang"]

Thanks.

William Elliot wrote:
> On Tue, 31 Oct 2006, Yajun  Wang wrote:
>
> > We have set A subset R^2, and its complement B. If both of them are star
> > shaped, is it possible to show that their boundary is homeomorphic to an
> > open line segment?
> >
> > There are other properties available, e.g, one of them is open set.
>
> No.  B = [-1,0]x{0} \/ [0,oo)xR with open complement
> has boundary that isn't homeomorphic to any line segment.