Inverse Limits of Hausdorff Arcs - Smith, Michel (Topology Proceedings, 2026)
We prove that if $X$ is an inverse limit of Hausdorff arcs and $X$ is a hereditarily indecomposable continuum, then each coordinate arc has countable cellularity (satisfies the countable chain condition). From this theorem and previous results it follows that if $X$ is an inverse limit of Hausdorff arcs and $M \subset X$ is a hereditarily indecomposable continuum, then $M$ is a metric continuum.