\(\epsilon\)-isometries in Euclidean spaces (Q2581735)

The author considers the \(n\)-dimensional Euclidean space \(E_{n}\) and an \(\epsilon\)-isometry \(f\) of a special bounded subset \(A \subset E_{n}\) into \(E_{n}\), i.e. \(\| f(y)-f(x)\| -\| y-x\| \leq \epsilon\) for all \(x,y\in A\). He shows how close is \(f\) to an affine isometry.