%0 Journal Article
%J Journal of Electrical Engineering
%D 2001
%T A "Converse" of the Bananch Contraction Mapping Theorem
%A Pascal Hitzler
%A Anthony K. Seda
%K Banach contraction
%K Banach contraction mapping theorem
%X We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T_{1} topological space and *f*: X -> X is a function with the unique fixed point *a* such that *f*^{n}(*x*) converges to *a* for each *x* is a member of *X*, then there exists a distance function *d* on *X* such that *f* is a contraction on the complete ultrametric space (X,d) with contractivity factor 1/2. We explore properties of the resulting space (X,d).
%B Journal of Electrical Engineering
%P 3-6
%G eng