afgrænset

Afgrænset is a Danish adjective meaning bounded, delimited, or restricted, depending on context. In everyday use it describes something with clearly defined borders, such as a afgrænset område (a defined area) or en afgrænset ansvarsområde (clearly delimited responsibilities). In mathematics the term has a precise technical meaning: a set is afgrænset if it lies within a finite region of space. Formally, in a metric space, a subset S is afgrænset if there exists a point x0 and a real number R such that the distance from x to x0 is less than R for every x in S. In Euclidean space this is equivalent to saying that the diameter of S is finite. For example, the closed interval [a, b] is afgrænset, while the unbounded set (0, ∞) is not. Boundedness is a common condition in theorems, such as those characterizing compact subsets in R^n, where compactness requires afgrænsetness (boundedness) together with closedness.

In other domains, afgrænset often refers to clearly drawn borders or limits, such as a demarcated region in geographic planning or a project’s scope that is defined and constrained. Etymology: afgrænset derives from af- (“away, off”) and grænse (“border, boundary”), reflecting the sense of being cut off by borders. Related terms include afgrænsning (the act of delimitation), grænse (border), and begrænset (limited, with a more general sense of restriction). The term is widely used in Danish mathematics and public discourse to express explicit borders or limits.