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

[William Elliot]

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.