Embeddings of the pseudo-arc in<i>E</i>²

Abstract

In this paper, we show that there exists an embedding, P s , of 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 o distinct embeddings of the pseudo-arc in the plane, including for each positive integer n, one with exactly n composants accessible. This answers some questions and a conjecture of Brechner.