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  • In [[mathematics]], a '''bounded set''' is any [[set|subset]] of a [[normed space]] whose elements all have norm Every bounded set of [[real number]]s has a [[supremum]] and an [[infimum]]. It follows that
    1 KB (188 words) - 05:37, 29 December 2008
  • {{r|Bounded set}} {{r|Totally bounded set}}
    531 bytes (72 words) - 14:37, 31 October 2008
  • ...ce]], a subset is compact if and only if it is [[closed set|closed]] and [[bounded set|bounded]]. ...lds: a subset is compact if and only if it is [[closed set|closed]] and [[bounded set|bounded]].
    2 KB (381 words) - 08:54, 29 December 2008
  • a ''finite interval'' and a ''bounded set'' because its ''length'' is bounded,
    1 KB (191 words) - 17:30, 15 July 2009
  • ...]], such as the Euclidean spaces, total boundedness is ''equivalent'' to [[bounded set|boundedness]].
    975 bytes (166 words) - 15:27, 6 January 2009
  • {{r|Bounded set}} {{r|Totally bounded set}}
    565 bytes (76 words) - 19:05, 11 January 2010
  • {{r|Bounded set}} {{r|Totally bounded set}}
    942 bytes (125 words) - 18:29, 11 January 2010
  • ...ess is equivalent to the set being [[completeness|complete]] and [[totally bounded set|totally bounded]] and again equivalent to [[sequential compactness]]: that ...an space]]s, then compactness is equivalent to that set being closed and [[bounded set|bounded]]: this is the [[Heine-Borel theorem]].
    4 KB (652 words) - 14:44, 30 December 2008
  • {{r|Totally bounded set}}
    322 bytes (45 words) - 13:51, 26 July 2008
  • {{r|Bounded set}}
    576 bytes (77 words) - 19:04, 11 January 2010
  • #The space of the [[equivalence class]] of all real valued [[bounded set|bounded]] [[Lebesgue measurable]] functions on the interval [0,1] with the
    982 bytes (148 words) - 07:17, 3 December 2007
  • is the boundary of an interior bounded set which it separates from the (unbounded) exterior.
    2 KB (394 words) - 04:46, 5 October 2009
  • The fundamental axiom for the real numbers is that every non-empty bounded set has a supremum and an infimum.
    3 KB (538 words) - 18:17, 17 January 2010
  • ...[[real number|real]] sequences, a monotonic sequence converges if it is [[bounded set|bounded]]. Every real sequence has a monotonic subsequence.
    1 KB (211 words) - 17:02, 7 February 2009
  • {{r|Bounded set}}
    681 bytes (91 words) - 18:06, 11 January 2010
  • Example 2. Every bounded set of real numbers has its least upper bound. More formally: for every subset
    21 KB (3,291 words) - 16:07, 3 November 2013
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