What does uniform continuity mean?
Definitions for uniform continuity
uni·for·m con·ti·nu·ity
This dictionary definitions page includes all the possible meanings, example usage and translations of the word uniform continuity.
Wiktionary
uniform continuitynoun
The property of being uniformly continuous.
Wikidata
Uniform continuity
In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f(x) and f be as close to each other as we please by requiring only that x and y are sufficiently close to each other; unlike ordinary continuity, the maximum distance between f(x) and f cannot depend on x and y themselves. For instance, any isometry between metric spaces is uniformly continuous. Every uniformly continuous function between metric spaces is continuous. Uniform continuity, unlike continuity, relies on the ability to compare the sizes of neighbourhoods of distinct points of a given space. In an arbitrary topological space this may not be possible. Instead, uniform continuity can be defined on a metric space where such comparisons are possible, or more generally on a uniform space. The equicontinuity of a set of functions is a generalization of the concept of uniform continuity. Every continuous function on a compact set is uniformly continuous.
Numerology
Chaldean Numerology
The numerical value of uniform continuity in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of uniform continuity in Pythagorean Numerology is: 3
Translations for uniform continuity
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"uniform continuity." Definitions.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.definitions.net/definition/uniform+continuity>.
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