  Let R be a ring and X = SH(R)-{0} be the set of all non-zero strongly hollow
ideals (briefly, sh-ideals) of R. We first study the concept SH-topology and
investigate some of the basic properties of a topological space with this
topology. It is shown that if X is with SH-topology, then X is Noetherian if
and only if every subset of X is quasi-compact if and only if R has dcc on
semi-sh-ideals.
  Finally, the relation between the dual-classical Krull dimension of R and the
derived dimension of X with a certain topology has been studied. It is proved
that, if X has derived dimension, then R has the dual-classical krull dimension
and in case R is a D-ring (i.e., the lattice of ideals of R is distributive),
then the converse is true. Moreover these two dimension differ by at most 1.
