Abstract:
This paper presents an extension of Hubert's incidence axioms to n dimensions and uses these and his order axioms to prove several theorems. We prove extensions of Pasch's Axiom, the Crossbar Theorem, and Desargues' Theorem for n dimensions. A non-Euclidean model is presented and proved to satisfy the axioms. In the last chapter we define n-polytope (n-dimensional complex) and prove, from the axioms given, that every n-polytope can be dissected into n-simplices.
