On Extension of Isomeries in (F)- Spaces

An (F)- space E is said to be locally midpoint constricted (in short, lmp-constricted) if there exists some d (delta) >0 such that D(A/2) < D(A) for every subset A of E with 0< D(A/2) <= d (delta), where D(A) denotes the diameter of A. Our main result goes as follow: Let E be an lmp-constricted (F)-space and U an open connected subset of E. Assume that T: U -> F in an isometry (i.e., a distance-preserving map) which maps U onto an open subset of the (F)-space F. Then T can be extendet to an affine homeomorphis from E to F. Also, some other results about the question whether each isometry between two (F)-space is affine are obtain.