Boundedness
Encyclopedia
Boundedness or bounded may refer to:
- Bounded setBounded setIn mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded...
, a set that is finite in some sense - Bounded functionBounded functionIn mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded. In other words, there exists a real number M...
, a function or sequence whose possible values form a bounded set - Bounded poset a partially ordered set which has both a greatest element and a least element
- Bounded set (topological vector space)Bounded set (topological vector space)In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set...
, a set in which every neighborhood of the zero vector can be inflated to include the set - Bounded operatorBounded operatorIn functional analysis, a branch of mathematics, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L to that of v is bounded by the same number, over all non-zero vectors v in X...
, a linear transformation L between normed vector spaces for which the ratio of the norm of L(v) to that of v is bounded by the same number, over all non-zero vectors v - Bounded variationBounded variationIn mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded : the graph of a function having this property is well behaved in a precise sense...
, a real-valued functions whose total variation is bounded - Boundedness axiom, the axiom schema of replacement
- Boundedness (linguistics)Boundedness (linguistics)In linguistics, boundedness is an aspectual feature that describes a situation as having a definite beginning or end, or both, not as continuing indefinitely. Thus the clause "I ate fish" describes a unitary, bounded action, as it implies both the beginning and the end...
, whether a situation has a clearly defined beginning or end