... DOMAINS535 The main result of the next two sections is the following theorem (Γ1(∂)is the component of B1∩ Γ containing B1∩ ∂Γ):Theorem II.1.2 (see Figure 9). Given N, τ > 0, there exist ... Rado’s theorem (note that no assumption on the topologyis needed for this application of Rado’s theorem; cf. the proof of theorem 1.22in [CM4]), Σ0,tis itself a graph, giving the lemma. The ... we seethat the proof of Theorem 0.3 will also give (if 0 ∈ Σ, then Σ0,tdenotes the component of Bt∩ Σ containing 0):Theorem 0.5. Given C, there exist C2,C3> 1, so that the followingholds:Let...