Maybe Jim could elaborate on how the desired concept relates to convexity. —Dan ----- This is a little bit different from what I was asking about, though it's also interesting. Dan's notion is about X being convex relative to some bigger set M; I'm asking about X being convex relative to some smaller set Y. In the case where the smaller set is just a point p, the natural notion of "convex relative to {p}" might be "starlike from p". ... ...
Jim Propp wrote: ----- Is there a notion of "relative convexity" that would make an ordinary torus consisting of points at small fixed distance from a large circle "convex relative to the circle"?
Thinking about different sorts of polyhedral tori people have come up with, I realize that part of what I want esthetically is some kind of relative convexity, but I don't know what it should mean! -----