Article contents
Locally Convex Hypersurfaces
Published online by Cambridge University Press: 20 November 2018
Extract
Let M be an n-dimensional connected topological manifold. Let ξ : M → Rn+1 be a continuous map with the following property: to each x ∈ M there is an open set x ∈ Ux ⊂ M, and a convex body Kx ⊂ Rn+1 such that ξ(UX) is an open subset of ∂Kx and such that is a homeomorphism onto its image. We shall call such a mapping ξ a locally convex immersion and, along with Van Heijenoort [8] we shall call ξ(M) a locally convex hypersurface of Rn+1.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1973
References
- 4
- Cited by