  The class of special generic maps contains Morse functions with exactly two
singular points, characterizing spheres topologically which are not
$4$-dimensional and the $4$-dimensional unit sphere. This class is for higher
dimensional versions of such functions. Canonical projections of unit spheres
are simplest examples and suitable manifolds diffeomorphic to ones represented
as connected sums of products of spheres admit such maps. They have been found
to restrict the topologies and the differentiable structures of the manifolds
strongly.
  The present paper focuses on images of special generic maps on closed
manifolds. They are smoothly immersed compact manifolds whose dimensions are
same as those of the targets. Some studies imply that they have much
information on homology groups and cohomology rings. We present new
construction and explicit examples of special generic maps by investigating the
images and the present paper is essentially on construction and explicit
algebraic topological and differential topological studies of immersed compact
manifolds.
