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Continuous Geometry
John von Neumann
With a foreword by Israel Halperin

Book Description | Reviews

TABLE OF CONTENTS:

Foreword
Foundations and Elementary Properties1
Independence8
Perspectivity and Projectivity. Fundamental Properties16
Perspectivity by Decomposition24
Distributivity. Equivalence of Perspectivity and Projectivity32
Properties of the Equivalence Classes42
Dimensionality54
Theory of Ideals and Coordinates in Projective Geometry63
Theory of Regular Rings69
Appendix 182
Appendix 284
Appendix 390
Order of a Lattice and of a Regular Ring93
Isomorphism Theorems103
Projective Isomorphisms in a Complemented Modular Lattice117
Definition of L-Numbers; Multiplication130
Appendix133
Addition of L-Numbers136
Appendix148
The Distributive Laws, Subtraction; and Proof that the L-Numbers form a Ring151
Appendix158
Relations Between the Lattice and its Auxiliary Ring160
Further Properties of the Auxiliary Ring of the Lattice168
Special Considerations. Statement of the Induction to be Proved177
Treatment of Case I191
Preliminary Lemmas for the Treatment of Case II197
Completion of Treatment of Case II. The Fundamental Theorem199
Perspectivities and Projectivities209
Inner Automorphisms217
Properties of Continuous Rings222
Rank-Rings and Characterization of Continuous Rings231
Center of a Continuous Geometry240
Appendix 1245
Appendix 2259
Transitivity of Perspectivity and Properties of Equivalence Classes264
Minimal Elements277
List of Changes from the 1935-37 Edition and comments on the text by Israel Halperin283
Index297

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File created: 7/11/2014

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