closure properties

closure properties
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  • Closure with a twist — is a property of subsets of an algebraic structure. A subset Y of an algebraic structure X is said to exhibit closure with a twist if for every two elements there exists an automorphism ϕ of X and an element such that …   Wikipedia

  • Closure (topology) — For other uses, see Closure (disambiguation). In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are near S. A point which is in the… …   Wikipedia

  • Closure operator — In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. X ⊆ cl(X) (cl is extensive) X ⊆ Y implies cl(X) ⊆ cl(Y)   (cl… …   Wikipedia

  • Closure (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …   Wikipedia

  • Closure (atmospheric science) — A closure experiment in atmospheric science is a combination of different measurement techniques to describe the current state of the investigated system as fully as possible, and to find inaccuracies in one or some of the methods involved. The… …   Wikipedia

  • Kuratowski closure axioms — In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms which can be used to define a topological structure on a set. They are equivalent to the more commonly used open set definition. They were first… …   Wikipedia

  • Causal closure — is a metaphysical theory about the nature of causation in the physical realm with significant ramifications in the study of the mind.DefinitionCausal closure has two main formulations a weak and a strong form. The weak form states: No physical… …   Wikipedia

  • Medicinal properties of dandelion — Dandelions may have medicinal properties. Definition The common dandelion, taraxacum officinale , is a weed that is often considered a nuisance and to give lawns an unkempt look, but it is a versatile item in both the kitchen and as a medicinal… …   Wikipedia

  • Integrality — In commutative algebra, the notions of an element integral over a ring (also called an algebraic integer over the ring), and of an integral extension of rings, are a generalization of the notions in field theory of an element being algebraic over …   Wikipedia

  • Complexity class — In computational complexity theory, a complexity class is a set of problems of related resource based complexity. A typical complexity class has a definition of the form: the set of problems that can be solved by an abstract machine M using… …   Wikipedia

  • Transitive relation — In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b , and b is in turn related to an element c , then a is also related to c . Transitivity is a key property of both partial order… …   Wikipedia


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