Continuous geometry

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 , it can be an element of the unit interval . 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.

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