Lipschitz mappings on the unit sphere of an infinite-dimensional normed space (Q1865240)

Given an infinite-dimensional normed space \(X\) with unit sphere \(S(X)\), the authors prove that there exists a Lipschitz continuous map \(f:S(x)\to S(x)\) such that \(\inf\{\|f(x)\pm x\|:x\in S(x)\}>0\).