unique. Mathematics portal Weisstein, Eric W. "Transitive Closure". mathworld.wolfram.com. Retrieved 2020-07-25. Weisstein, Eric W. "Algebraic Closure". mathworld...

axioms for its use in database theory Closure (mathematics), the result of applying a closure operator Closure (topology), for a set, the smallest closed...

closed in Wiktionary, the free dictionary. Closed may refer to: Closure (mathematics), a set, along with operations, for which applying those operations...

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one...

In programming languages, a closure, also lexical closure or function closure, is a technique for implementing lexically scoped name binding in a language...

In mathematics, a closure operator on a set S is a function cl : P ( S ) → P ( S ) {\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal...

In mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive...

In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms that can be used to define a topological structure...

The term normal closure is used in two senses in mathematics: In group theory, the normal closure of a subset of a group is the smallest normal subgroup...

topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may...

In mathematics, specifically in topology, the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point...

general mathematical concept of closure — in particular, the deductive closure of ⁠ T {\displaystyle {\mathcal {T}}} ⁠ is exactly the closure of ⁠ T {\displaystyle...

theory. Some of the notable mathematical concepts bearing Kuratowski's name include Kuratowski's theorem, Kuratowski closure axioms, Kuratowski-Zorn lemma...

x ≤ f(x). These have many applications in all kinds of "closures" that appear in mathematics. Besides being compatible with the mere order relations,...

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on...

operator is the closure operator C defined by xC = ((x′)I)′. xC is called the closure of x. By the principle of duality, the closure operator satisfies...

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation...

In group theory, the normal closure of a subset S {\displaystyle S} of a group G {\displaystyle G} is the smallest normal subgroup of G {\displaystyle...

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining...

mathematics, a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure is...

In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number...

In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on...

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern...

notion of n-ary group. Mathematics portal List of group theory topics Some authors include an additional axiom referred to as the closure under the operation...

the Frobenius endomorphism x ↦ xp is an automorphism of k. The separable closure of k is algebraically closed. Every reduced commutative k-algebra A is...

In mathematics, in the area of commutative algebra, tight closure is an operation defined on ideals in positive characteristic. It was introduced by Melvin...

In mathematics, the reflexive closure of a binary relation R {\displaystyle R} on a set X {\displaystyle X} is the smallest reflexive relation on X {\displaystyle...

Digraphs, Transitive Closures and Reductions", Digraphs: Theory, Algorithms and Applications, Springer Monographs in Mathematics, Springer, pp. 36–39...

T.; Kortelainen, J. (2007). Transitive Closures of Binary Relations I (PDF). Prague: School of Mathematics – Physics Charles University. Archived from...

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...