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mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic...

or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets). Borel sets are important...

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 unions...

Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets. A field...

The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator:...

logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true...

Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization...

mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting...

mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically...

non-irreducible algebraic varieties are called algebraic sets. Other conventions do not require irreducibility. The fundamental theorem of algebra establishes...

properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its...

algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are...

negation. Applications include the propositional calculus and the theory of digital circuits. The algebra of sets under the set operations including union...

X} ). Algebra of sets – Identities and relationships involving sets δ-ring – Ring closed under countable intersections Field of sets – Algebraic concept...

is a list of topics around Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective...

of the area into maturity. The topological setting for nonlinear algebra is typically the Zariski topology, where closed sets are the algebraic sets....

Singleton (mathematics) Simple theorems in the algebra of sets Algebra of sets Power set Empty set Non-empty set Empty function Universe (mathematics) Axiomatization...

corresponds to the Unicode symbol U+2201 ∁ COMPLEMENT.) Algebra of sets – Identities and relationships involving sets Intersection (set theory) – Set of elements...

mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with...

themselves) σ-algebra – Algebraic structure of set algebra σ-ring – Family of sets closed under countable unions P. Halmos, Naive Set Theory, p.34. The University...