metric continuity

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• 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

• Metric (mathematics) — In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric …   Wikipedia

• metric space — Math. a space with a metric defined on it. [1925 30] * * * In mathematics, a set of objects equipped with a concept of distance. The objects can be thought of as points in space, with the distance between points given by a distance formula, such… …   Universalium

• Modulus of continuity — In mathematical analysis, a modulus of continuity is a function used to measure quantitatively the uniform continuity of functions. So, a function admits ω as a modulus of continuity if and only if for all x and y in the domain of f. Since moduli …   Wikipedia

• Uniform continuity — In mathematical analysis, a function f ( x ) is called uniformly continuous if, roughly speaking, small changes in the input x effect small changes in the output f ( x ) ( continuity ), and furthermore the size of the changes in f ( x ) depends… …   Wikipedia

• Lipschitz continuity — In mathematics, more specifically in real analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a smoothness condition for functions which is stronger than regular continuity. Intuitively, a Lipschitz continuous function is limited in… …   Wikipedia

• Absolute continuity — In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using… …   Wikipedia

• Disaster recovery and business continuity auditing — Disaster recovery and business continuity refers to an organization’s ability to recover from a disaster and/or unexpected event and resume or continue operations. Organizations should have a plan in place (usually referred to as a Disaster… …   Wikipedia

• Semi-continuity — For the notion of upper or lower semicontinuous multivalued function see: Hemicontinuity In mathematical analysis, semi continuity (or semicontinuity) is a property of extended real valued functions that is weaker than continuity. A extended real …   Wikipedia

• Dini continuity — In mathematical analysis, Dini continuity is a refinement of continuity. Contents 1 Definition 2 Properties 3 See also 4 References …   Wikipedia

• sequential continuity — noun The property of a function between metric spaces, that given a convergent sequence , then , i.e. the property of a function that it preserves sequential convergence …   Wiktionary