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Filtering by: Subject Hilbert space Remove constraint Subject: Hilbert space Advisor Goheen, Harry Remove constraint Advisor: Goheen, Harry Creator Murray, Peter John Remove constraint Creator: Murray, Peter John

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

    Creator:
    Murray, Peter John
    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...
    Resource Type:
    Dissertation
    Full Text:
    N DIMENSIONS I. INTRODUCTION In 1898, David Hilbert published a set of axioms for plane and 3