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bounded below if all modules below some fixed degree are 0. Clearly, a complex is bounded both above and below if and only if the complex is bounded....

some set X {\displaystyle X} with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number...

boundary, C1 boundary, and so forth. A bounded domain is a domain that is bounded, i.e., contained in some ball. Bounded region is defined similarly. An exterior...

convergence theorem is the bounded convergence theorem, which states that if (fn) is a sequence of uniformly bounded complex-valued measurable functions...

perfect complex of modules over a commutative ring A is an object in the derived category of A-modules that is quasi-isomorphic to a bounded complex of finite...

actions. In another work, he states "boundedly rational agents experience limits in formulating and solving complex problems and in processing (receiving...

bounded if it is bounded around every point. A family of functions is locally bounded if for any point in their domain all the functions are bounded around...

counterparts. According to Liouville's theorem, any bounded complex analytic function defined on the whole complex plane is constant. The corresponding statement...

{\displaystyle Y} is Banach. Bounded set (topological vector space) – Generalization of boundedness Contraction (operator theory) – Bounded operators with sub-unit...

coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds...

In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is...

in complex analysis is the line integral. The line integral around a closed path of a function that is holomorphic everywhere inside the area bounded by...

type of erythema possibly mediated by deposition of immune complexes (mostly IgM-bound complexes) in the superficial microvasculature of the skin and oral...

] dictates. For example, Froissart bound says that the total cross section of two particles scattering is bounded by c ln 2 ⁡ s {\displaystyle c\ln ^{2}s}...

to Complex IV (cytochrome c oxidase; labeled IV). Four membrane-bound complexes have been identified in mitochondria. Each is an extremely complex transmembrane...

analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite): the graph of...

(although the theorem was first proven by Cauchy in 1844), states that every bounded entire function must be constant. That is, every holomorphic function f...

defined on the Banach space ℓ ∞ {\displaystyle \ell ^{\infty }} of all bounded complex-valued sequences such that for all sequences x = ( x n ) {\displaystyle...

{\displaystyle K_{0}(X)} of bounded complexes of coherent sheaves is canonically isomorphic to the Grothendieck group of bounded complexes of finite-rank vector...

Formally, the bounded Borel functional calculus of a self adjoint operator T on Hilbert space H is a mapping defined on the space of bounded complex-valued Borel...