[Someone]

> Ok, wikipedia makes it clearer:

> "In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction."

Is that definition correct/complete? It leaves open the option that such a set isn’t connected. I think there’s an additional requirement that, for any two directions D and E, you can move a line segment oriented in direction D so that it’s oriented in direction E without any point on it ever leaving the set.

[shiandow]

The minimal set is trivially connected. Though showing any two unit line segments have a homology between them is trickier.