In 1972, Nadler and Quinn asked if for any arc-like continuum $X$, and point $x\in X$, there exists a plane embedding of $X$ in which $x$ is accessible. A continuum $X$ is arc-like if it can be expressed as an inverse limit on arcs and, if $X$ is in the plane ${\mathbb{R}}^2$, a point $x\in X$ is called accessible if there exists an arc $A\subset {\mathbb{R}}^2$ such that $A\cap X=$ {$x$}. The question was recently answered in the positive (AA, Anušić, Hoehn 2024). This talk will discuss some consequences of the result: if $X$ is an arc-like continuum, then any continuum which is the disjoint union of $X$ and a ray $R$, with cl$(R)\setminus R\subseteq X$, is embeddedable in the plane, as is any compactification of a line having remainder $X$.

Joint work with Logan Hoehn.