On the division of Euclidean n -space by topological ( n ─ 1)-spheres
M. H. A. Newman · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1960
Abstract Mazur’s theorem on the division of an n-sphere is generalized and applied to show that closed Euclidean n-space is split into two n-cells by an embedded topological (n ─ 1)-sphere, S, if either S has a continuously varying tangent hyperplane, or S is a rectilinearly embedded complex in which the link of every simplex is a topological sphere.