  As it was shown in the first part of this paper, there exists a duality
between the category DSkeLC (introduced there) and the category SkeLC of
locally compact Hausdorff spaces and continuous skeletal maps. We describe here
the subcategories of the category DSkeLC which are dually equivalent to the
following eight categories: all of them have as objects the locally compact
Hausdorff spaces and their morphisms are, respectively, the injective
(respectively, surjective) continuous skeletal maps, the injective (resp.,
surjective) open maps, the injective (resp., surjective) skeletal perfect maps,
the injective (resp., surjective) open perfect maps. The particular cases of
these theorems for the full subcategories of the last four categories having as
objects all compact Hausdorff spaces are formulated and proved. The
DSkeLC-morphisms which are LCA-embeddings and the dense homeomorphic embeddings
are characterized through their dual morphisms. For any locally compact space
X, a description of the frame of all open subsets of X in terms of the dual
object of X is obtained. It is shown how one can build the dual object of an
open subset (respectively, of a regular closed subset) of a locally compact
Hausdorff space X directly from the dual object of X. Applying these results, a
new description of the ordered set of all, up to equivalence, locally compact
Hausdorff extensions of a locally compact Hausdorff space is obtained.
Moreover, generalizing de Vries Compactification Theorem, we strengthen the
Local Compactification Theorem of Leader. Some other applications are found.
