 After indicating important similarities between his and von Neumann’s approaches to infinite quantum systems, Segal draws an important contrast that serves to give the advantage to his approach over von Neumann’s. The key mathematical difference, according to Segal, is that von Neumann was working with a weakly closed ring of operators (meaning that the ring of operators is closed with respect to the weak operator topology), whereas Segal is working with a uniformly closed ring of operators (closed with respect to the uniform topology). It is crucial because it has the following interpretive significance, which rests on operational considerations: