Boundedness

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Boundedness or bounded may refer to:

• Bounded set in a metric space, a set with a (finite) upper bound on the distance between its points
• Bounded function, 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), 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

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Verb

bounded

1. Simple past tense and past participle of bound.

Adjective

bounded (comparative more bounded, superlative most bounded)

1. (analysis) Of a set, that it is capable of being included within a ball of finite radius.

   A compact set must be bounded.

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