  We derive some more results on the nature of the singularities arising in the
collapse of inhomogeneous dust spheres. (i) It is shown that there are
future-pointing radial and non-radial time-like geodesics emerging from the
singularity if and only if there are future-pointing radial null geodesics
emerging from the singularity. (ii) Limits of various space-time invariants and
other useful quantities (relating to Thorne's point-cigar-barrel-pancake
classification and to isotropy/entropy measures) are studied in the approach to
the singularity. (iii) The topology of the singularity is studied from the
point of view of ideal boundary structure. In each case, the different nature
of the visible and censored region of the singularity is emphasized.
