lukning

Lukning is a term used in Danish and Norwegian that refers to the act or result of closing something. In everyday language it can describe the physical act of closing a door or lid, as well as more abstract closures such as the end of an operation or the shutdown of a facility. In specialized contexts the word may take on more precise meanings depending on the field.

In mathematics, lukning denotes the topological closure of a set. Given a subset A of a topological space X, the lukning of A, usually written cl(A) or sometimes overline A, is the smallest closed set that contains A. Equivalently, it is the intersection of all closed supersets of A. The lukning operator is extensive (A ⊆ cl(A)), monotone (if A ⊆ B then cl(A) ⊆ cl(B)), and idempotent (cl(cl(A)) = cl(A)). In metric spaces, cl(A) can be described as A together with all its limit points. For example, in the real numbers with the standard topology, the lukning of the open interval (0, 1) is the closed interval [0, 1].

In addition to mathematics, lukning appears in medical contexts to describe the closure of wounds or surgical connections, and in everyday or industrial language to refer to closing something physically or administratively. Related concepts include interior, boundary, and the closure operator in topology.