00979nas a2200145 4500008004100000245006000041210005600101300000800157520053100165653002300696653003900719100002000758700002200778856003300800 2001 eng d00aA "Converse" of the Bananch Contraction Mapping Theorem0 aConverse of the Bananch Contraction Mapping Theorem a3-63 aWe 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).10aBanach contraction10aBanach contraction mapping theorem1 aHitzler, Pascal1 aSeda, Anthony, K. uhttp://knoesis.org/node/1631