To avoid unnecessary pitfalls we shall restrict our attention to a special kind of sets. This contradicts the first metric axiom . Y has a unique fixed point . I'll later explain with examples the utility of the two theorems and of the general framework offered by the metrization of families of sets for construction of fractals with the Iteration Function Systems . Here I only want to add a few words on the terminology used in the Contraction Mapping theorem.
Contraction mappings reduce distance between points.
Moreover, the following theorem holds Convergence Theorem Let f be a contraction mapping of a complete space Y into itself. Alexander Bogomolny 2791292 .