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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. |
