Hereditarily indecomposable subcontinua of inverse limits of Souslin arcs are metric

We prove that if S i is a Souslin arc (a Hausdorff arc that is the compactification of a Souslin line) for each i and X = lim ← { S i , f j i } j < i , then every hereditarily indecomposable subcontinuum of X is metric. Since every non-degenerate hereditarily indecomposable continuum that is an inverse limit on metric arcs is a pseudo-arc, it follows that such an X would be a pseudo-arc or a point.