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. COUNT 3
QSN1 What field did Von Neuman establish? ANS1 continuous geometry. QSN2 What is the distinction of continuous geometry? ANS2 instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit interval QSN3 What was the first example of continuous geometry? ANS3 projections of the hyperfinite type II factor