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bounded subset

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  • Bounded variation — In mathematical analysis, a function of bounded variation refers to a real valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a… …   Wikipedia

  • Bounded set — In 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. Definition A set S of real numbers is called bounded from …   Wikipedia

  • Bounded complete poset — In the mathematical field of order theory, a partially ordered set is bounded complete if all of its subsets which have some upper bound also have a least upper bound. Such a partial order can also be called consistently complete, since any upper …   Wikipedia

  • 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. Conversely a set which is not… …   Wikipedia

  • Bounded operator — In 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(v) to that of v is bounded by the same number, over all non zero… …   Wikipedia

  • Bounded (set theory) — In set theory a subset X of a limit ordinal lambda; is said to be bounded if its supremum is less than lambda;. If it is not bounded, it is unbounded, that is:sup(X)= lambda.,For functions, bounded or unboundedness refers to the range of the… …   Wikipedia

  • Bounded deformation — In mathematics, a function of bounded deformation is a function whose distributional derivatives are not quite well behaved enough to qualify as functions of bounded variation, although the symmetric part of the derivative matrix does meet that… …   Wikipedia

  • Totally bounded space — In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of any fixed size (where the meaning of size depends on the given context). The smaller the size fixed, the more… …   Wikipedia

  • Resource bounded measure — Lutz s resource bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of the Euclidean space R^n, resource… …   Wikipedia

  • Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… …   Wikipedia

  • Heine–Borel theorem — In the topology of metric spaces the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states:For a subset S of Euclidean space R n , the following two statements are equivalent: * S is closed and bounded *every open cover of S has a …   Wikipedia

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