Show that a set $F \subset \mathbb{R}^{n}$ with Hausdorff dimension strictly less than one is totally disconnected.

What does it mean for a Möbius transformation to pair two discs? By considering a pair of disjoint discs and a pair of tangent discs, or otherwise, explain in words why there is a 2-generator Schottky group with limit set $\Lambda \subset \mathbb{S}^{2}$ which has Hausdorff dimension at least 1 but which is not homeomorphic to a circle.