Read this: Von Neumann founded the field of continuous geometry. It followed his path-breaking work on rings of operators. In mathematics, continuous geometry is an analogue of complex projective geometry, 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.
Now answer this question, if there is an answer (If it cannot be answered, return "unanswerable"): What is the distinction of continuous geometry?
instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit interval