  The trichotomy between regular, semiregular, and strongly irregular boundary
points for $p$-harmonic functions is obtained for unbounded open sets in
complete metric spaces with a doubling measure supporting a $p$-Poincar\'e
inequality, $1<p<\infty$. We show that these are local properties. We also
deduce several characterizations of semiregular points and strongly irregular
points. In particular, semiregular points are characterized by means of
capacity, $p$-harmonic measures, removability, and semibarriers.
