The Existence of the Attractor of Countable Iterated Function Systems

The theory of iterated function systems (IFS) and of infinite iterated function systems consisting of contraction mappings has been studied in the last decades. Some extensions of the spaces and the contractions concern many authors in fractal theory. In this paper there are described some results in that topic concerning the existence and uniqueness of nonempty compact set which is a set ”fixed point” of a countable iterated function system (CIFS). Moreover, some approximations of the attractor of a CIFS by the attractors of the partial IFSs are given.