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About: Continuous geometry     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatVonNeumannAlgebrasyago:Abstraction100002137yago:Algebra106012726yago:Cognition100023271yago:Content105809192yago:Discipline105996646yago:KnowledgeDomain105999266yago:Mathematics106000644yago:PsychologicalFeature100023100yago:PureMathematics106003682drugyago:Science105999797 New Facet based on Instances of this Class

In mathematics, continuous geometry is an analogue of complex projective geometry introduced by von Neumann , where instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit interval [0,1]. Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor.