# Boundedness

Boundedness or bounded may refer to:

• Bounded set, a set that is finite in some sense
• Bounded function, a function or sequence whose possible values form a bounded set
• Bounded poset a partially ordered set that has both a greatest element and a least element
• Bounded set (topological vector space), a set in which every neighborhood of the zero vector can be inflated to include the set
• Bounded operator, 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 variation, a real-valued functions whose total variation is bounded
• Boundedness axiom, the axiom schema of replacement
• Boundedness (linguistics), whether a situation has a clearly defined beginning or end

### Other articles related to "boundedness":

Totally Bounded Space - Use of The Axiom of Choice
... The properties of total boundedness mentioned above rely in part on the axiom of choice ... In the absence of the axiom of choice, total boundedness and precompactness must be distinguished ... That is, we define total boundedness in elementary terms but define precompactness in terms of compactness and Cauchy completion ...
Mathematical Properties of Petri Nets - Boundedness
... Boundedness is decidable by looking at covering, by constructing the Karpâ€“Miller Tree. ...
Bounded Operator - Topological Vector Spaces
... The boundedness condition for linear operators on normed spaces can be restated ... set to a bounded set, and here is meant the more general condition of boundedness for sets in a topological vector space (TVS) a set is bounded if and only if it is absorbed by ... Note that the two notions of boundedness coincide for locally convex spaces ...
Mellin Inversion Theorem - Boundedness Condition
... We may strengthen the boundedness condition on if f(x) is continuous ... a generalized function, we may relax the boundedness condition on to simply make it of polynomial growth in any closed strip contained in the open strip ...
Totally Bounded Space - Relationships With Compactness and Completeness
... There is a nice relationship between total boundedness and compactness A uniform space is compact if and only if it is both totally bounded and Cauchy complete ... spaces to arbitrary spaces we must replace boundedness with total boundedness (and also replace closedness with completeness) ... There is a complementary relationship between total boundedness and the process of Cauchy completion A uniform space is totally bounded if and only if its Cauchy completion ...