  This paper discusses, certain algebraic, analytic, and topological results on
partial iterated function systems($IFS_p$'s). Also, the article proves the
Collage theorem for partial iterated function systems. Further, it provides a
method to address the points in the attractor of a partial iterated function
system and obtain results related to the address of points in the attractor.
The completeness of the partial metric space of contractions with a fixed
contractivity factor is proved, under suitable conditions. Also, it
demonstrates the continuity of the map that associates each contraction in a
complete partial metric space to its corresponding unique fixed point. Further,
it defines the $IFS_p$ semigroup and shows that under function composition, the
set of Lipschitz transformations and the set of contractions are semigroups.
