**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

... 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 is decidable by looking at covering, by constructing the Karpâ€“Miller Tree. ...

**Boundedness**... Boundedness is decidable by looking at covering, by constructing the Karpâ€“Miller Tree. ...

Bounded Operator - Topological Vector Spaces

... The

... 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 -

... We may strengthen the

**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

... 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 ...Main Site Subjects

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