  In this note, it is shown that several results concerning mean equicontinuity
proved before for minimal systems are actually held for general topological
dynamical systems. Particularly, it turns out that a dynamical system is mean
equicontinuous if and only if it is equicontinuous in the mean if and only if
it is Banach (or Weyl) mean equicontinuous if and only if its regionally
proximal relation is equal to the Banach proximal relation.
  Meanwhile, a relation is introduced such that the smallest closed invariant
equivalence relation containing this relation induces the maximal mean
equicontinuous factor for any system.
