On bijections of Lorentz manifolds, which leave the class of spacelike paths invariant (Q1071328)

The main purpose of this paper is to prove the following theorem: Let f be a bijection between Lorentzian manifolds such that f and \(f^{-1}\) preserve space-like paths. Then f is a homeomorphism with respect to the manifold topologies. Furthermore using results of \textit{D. B. Malament} [J. Math. Phys. 18, 1399-1404 (1977; Zbl 0355.53033)] it is shown that an S-homeomorphism (i.e. a homeomorphism with respect to the space topologies [see \textit{R. Göbel}, Mitt. Math. Ges. Hamb. 10, 763-771 (1980; Zbl 0571.53041)]) between time-orientable Lorentz manifolds is a conformal diffeomorphism.