Homeomorphisms of the Pseudoarc

We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fraïssé theoretic proofs of several important results, both old and new. Specifically, we recover Bing’s classic results on the uniqueness and homogeneity of the pseudoarc. We also show that the autohomeomorphism group of the pseudoarc has a dense conjugacy class, thus confirming a conjecture of Kwiatkowska.