The Nadler-Quinn problem on accessible points of arc-like continua

Abstract

We show that if X is an arc-like continuum, then for every point $x\in X$ there is a plane embedding of X in which x is an accessible point. This answers a question posed by Sam B. Nadler in 1972, which has become known as the Nadler-Quinn problem in continuum theory. Towards this end, we develop the theories of truncations and contour factorizations of interval maps. As a corollary, we answer a question of J.C. Mayer from 1982 about inequivalent plane embeddings of indecomposable arc-like continua.