Finite dimensional convex structures II: the invariants |
| |
Authors: | M. Van De Vel |
| |
Affiliation: | Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands |
| |
Abstract: | Various relations between the dimension and the classical invariants of a topological convex structure have been obtained, leading to an equivalence between Helly's and Carathéodory's theorem, and to the closedness of the hull of compact sets in finite-dimensional convexities. It is also shown that the Radon number of an n-dimensional binary convexity is in most cases equal to the Radon number of the n-cube, and a natural condition is presented under which the invariants are equal to dimension plus one. |
| |
Keywords: | Primary 54H99, 52A01, 52A35 Secondary: 54F45 |
本文献已被 ScienceDirect 等数据库收录! |
|