منابع مشابه
Von Neumann and Lattice Theory
1. Introduction. John von Neumann's brilliant mind blazed over lattice theory like a meteor, during a brief period centering around 1935-1937. With the aim of interesting him in lattices, I had called his attention, in 1933-1934, to the fact that the sublattice generated by three subspaces of Hubert space (or any other vector space) contained 28 subspaces in general, to the analogy between dime...
متن کاملQuantum Hall Dynamics on Von Neumann Lattice
h in quantum Hall regime of the system of interactions and disorders. This shows that a determination of the fine structure constant from integer quantum Hall effect is in fact possible. We present also a unified mean field theory of the fractional Hall effect for the in-compressible quantum liquid states based on flux condensation and point out that the known Hofstadter butterfly spectrum of t...
متن کاملCantor-von Neumann Set-theory
In this elementary paper we establish a few novel results in set theory; their interest is wholly foundational-philosophical in motivation. We show that in Cantor-Von Neumann Set-Theory, which is a reformulation of Von Neumann’s original theory of functions and things that does not introduce ‘classes’ (let alone ‘proper classes’), developed in the 1920ies, both the Pairing Axiom and ‘half’ the ...
متن کاملSet Theory and von Neumann algebras
The aim of the lectures is to give a brief introduction to the area of von Neumann algebras to a typical set theorist. The ideal intended reader is a person in the field of (descriptive) set theory, who works with group actions and equivalence relations, and who is familiar with the rudiments of ergodic theory, and perhaps also orbit equivalence. This should not intimidate readers with a differ...
متن کاملVon Neumann on Measure and Ergodic Theory
According to a currently popular principle of classification, mathematics is the study of various "categories. " A category consists of certain "objects" (e.g., groups, topological spaces) and certain "mappings" (e.g., homomorphisms, continuous functions). One possible category has measure spaces for its objects and, correspondingly, measure-preserving transformations for its mappings. The usua...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1958
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1958-10192-5