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...
18 KB (2,664 words) - 01:33, 18 April 2024
operations individually. The closure of a subset is the result of a closure operator applied to the subset. The closure of a subset under some operations...
12 KB (1,772 words) - 15:53, 2 April 2024
interior operator. Let X {\displaystyle X} be an arbitrary set and ℘ ( X ) {\displaystyle \wp (X)} its power set. A Kuratowski closure operator is a unary...
30 KB (3,764 words) - 18:08, 9 October 2023
abstract theory of closure operators and the Kuratowski closure axioms can be readily translated into the language of interior operators by replacing sets...
27 KB (4,293 words) - 20:13, 5 October 2023
axioms for its use in database theory Closure (mathematics), the result of applying a closure operator Closure (topology), for a set, the smallest closed...
5 KB (576 words) - 10:55, 10 August 2024
Interior algebra (redirect from Closure algebra)
interior 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...
30 KB (3,849 words) - 16:32, 8 April 2024
Convex hull (redirect from Convex closure)
The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets...
61 KB (7,148 words) - 23:26, 8 August 2024
Kleene star (redirect from Kleene closure)
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 sets of...
7 KB (1,013 words) - 16:52, 18 July 2023
Idempotence (redirect from Idempotent operator)
abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property...
22 KB (2,887 words) - 01:11, 16 July 2024
Interior (topology) (category Closure operators)
operator below or the article Kuratowski closure axioms. The interior operator int X {\displaystyle \operatorname {int} _{X}} is dual to the closure operator...
14 KB (2,250 words) - 05:50, 12 February 2024