  We prove that dagger closure is trivial in regular domains containing a field
and that graded dagger closure is trivial in polynomial rings over a field. We
also prove that Heitmann's full rank one closure coincides with tight closure
in positive characteristic under some mild finiteness conditions. Furthermore,
we prove that dagger closure is always contained in solid closure and that the
forcing algebra for an element contained in dagger closure is parasolid.
