closed subset
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Closed set — This article is about the complement of an open set. For a set closed under an operation, see closure (mathematics). For other uses, see Closed (disambiguation). In geometry, topology, and related branches of mathematics, a closed set is a set… … Wikipedia
Closed operator — In mathematics, specifically in functional analysis, closed linear operators are an important class of linear operators on Banach spaces. They are more general than bounded operators, and therefore not necessarily continuous, but they still… … Wikipedia
Closed linear span — In functional analysis, a branch of mathematics, the closed linear span of a set of vectors is the minimal closed set which contains the linear span of that set. Contents 1 Definition 2 Notes 3 A useful lemma … Wikipedia
Closed world assumption — The closed world assumption (CWA) is the presumption that what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed world assumption is… … Wikipedia
Closed and exact differential forms — In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form that is the exterior derivative of another … Wikipedia
closed — adjective Date: 13th century 1. a. not open b. enclosed c. composed entirely of closed tubes or vessels < a closed circulatory system > 2. a. forming a self contained unit allowing no additions … New Collegiate Dictionary
Multiplicatively closed set — In abstract algebra, a subset of a ring is said to be multiplicatively closed if it is closed under multiplication (i.e., xy is in the set when x and y are in it) and contains 1 but doesn t contain 0.[1] The condition is especially important in… … Wikipedia
Differentially closed field — In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by Robinson (1959).… … Wikipedia
Cartesian closed category — In category theory, a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in… … Wikipedia
Open and closed maps — In topology, an open map is a function between two topological spaces which maps open sets to open sets.[1] That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function… … Wikipedia
Integrally closed domain — In commutative algebra, an integrally closed domain A is an integral domain whose integral closure in the field of fractions of A is A itself. Many well studied domains are integrally closed: Fields, the ring of integers Z, unique factorization… … Wikipedia
