Continuous Geometry
John von Neumann
With a foreword by Israel Halperin

Book Description | Reviews

TABLE OF CONTENTS:

	Foreword
	Foundations and Elementary Properties	1
	Independence	8
	Perspectivity and Projectivity. Fundamental Properties	16
	Perspectivity by Decomposition	24
	Distributivity. Equivalence of Perspectivity and Projectivity	32
	Properties of the Equivalence Classes	42
	Dimensionality	54
	Theory of Ideals and Coordinates in Projective Geometry	63
	Theory of Regular Rings	69
	Appendix 1	82
	Appendix 2	84
	Appendix 3	90
	Order of a Lattice and of a Regular Ring	93
	Isomorphism Theorems	103
	Projective Isomorphisms in a Complemented Modular Lattice	117
	Definition of L-Numbers; Multiplication	130
	Appendix	133
	Addition of L-Numbers	136
	Appendix	148
	The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring	151
	Appendix	158
	Relations Between the Lattice and its Auxiliary Ring	160
	Further Properties of the Auxiliary Ring of the Lattice	168
	Special Considerations. Statement of the Induction to be Proved	177
	Treatment of Case I	191
	Preliminary Lemmas for the Treatment of Case II	197
	Completion of Treatment of Case II. The Fundamental Theorem	199
	Perspectivities and Projectivities	209
	Inner Automorphisms	217
	Properties of Continuous Rings	222
	Rank-Rings and Characterization of Continuous Rings	231
	Center of a Continuous Geometry	240
	Appendix 1	245
	Appendix 2	259
	Transitivity of Perspectivity and Properties of Equivalence Classes	264
	Minimal Elements	277
	List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin	283
	Index	297

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