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The aim of this paper is to establish some results regarding InfiniteIterated Function Systems with the help of the Tarski-Kantorovitch fixed-pointprinciples for maps on partially ordered sets. To this end we introduce two newclasses of Infinite Iterated Function Systems which are well suited forapplying the aforementioned principle. We also study some properties of thecanonical projection from the shift space of an Infinite Iterated FunctionSystem belonging to one of the two introduced classes to its attractor.

Applications of the Tarski-Kantorovitch Fixed-Point Principle to the study of Infinite Iterated Function Systems