Embeddings of the pseudo-arc in E²

In this paper, we show that there exists an embedding, P_sof the pseudo-arc in the plane such that any two accessible points lie in distinct composants of P_s. We also show that there are c=2^ω0 distinct embeddings of the pseudo-arc in the plane, including for each positive integer n, one with exactly n composants accessible. This answerssome questions and a conjecture of Brechner.