mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable...

with the lower limit topology. A separable σ-algebra is a σ-algebra F {\displaystyle {\mathcal {F}}} that is a separable space when considered as a metric...

{\displaystyle A} a separable algebra over K {\displaystyle K} . It is useful to describe separability in terms of the element p := σ ( 1 ) = ∑ a i ⊗ b...

called the bidimension of A, measures the failure of separability. Let A be a finite-dimensional algebra over a field k. Then A is an Artinian ring. As A...

null set N and μ is a σ-finite measure) then L2(X, μ) is separable. The relationship between commutative von Neumann algebras and measure spaces is analogous...

Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets...

approximate identity and a C*-algebra with a sequential approximate identity is called σ-unital. Every separable C*-algebra is σ-unital, though the converse...

Neumann algebras are the direct integral of properly infinite factors. A von Neumann algebra that acts on a separable Hilbert space is called separable. Note...

If A is a separable C*-algebra, the weak-* topology is metrizable on bounded subsets. Thus the spectrum of a separable commutative C*-algebra A can be...

associative algebra over the field K {\displaystyle K} with Jacobson radical J {\displaystyle J} . Then A / J {\displaystyle A/J} is separable if and only...