Graduate Thesis Or Dissertation
 

An extension of Hilbert's axioms of incidence and order to n dimensions

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/mk61rm99q

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  • 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.
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