Continuous geometry

<p>In mathematics, continuous geometry is an analogue of complex <a href="/facts/Projective_geometry/rHKSaEbx">projective geometry</a> introduced  by <a href="/facts/John_von_Neumann/aUk6urof">von Neumann</a> (1936, 1998), where instead of the dimension of a subspace being in a discrete set 
  
    
      
        0
        ,
        1
        ,
        …
        ,
        
          
            n
          
        
      
    
    {\displaystyle 0,1,\dots ,{\textit {n}}}
  
, it can be an element of the unit interval 
  
    
      
        [
        0
        ,
        1
        ]
      
    
    {\displaystyle [0,1]}
  
. Von Neumann was motivated by his discovery of <a href="/facts/Von_Neumann_algebra/8NyWUIRH">von Neumann algebras</a> 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 <a href="/facts/Hyperfinite_type_II_factor/TAs9Q0sq">hyperfinite type II factor</a>.
</p>

Continuous geometry open-in-new

Continuous geometry