What does equicontinuity mean?
Definitions for equicontinuity
equicon·ti·nu·ity
This dictionary definitions page includes all the possible meanings, example usage and translations of the word equicontinuity.
Wiktionary
equicontinuitynoun
The condition of being equicontinuous
Wikidata
Equicontinuity
In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein. In particular, the concept applies to countable families, and thus sequences of functions. The equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of C, the space of continuous functions on a compact Hausdorff space X, is compact if and only if it is closed, pointwise bounded and equicontinuous. As a corollary, a sequence in C is uniformly convergent if and only if it is equicontinuous and converges pointwise to a function. In particular, the limit of an equicontinuous pointwise convergent sequence of continuous functions fn on either metric space or locally compact space is continuous. If, in addition, fn are holomorphic, then the limit is also holomorphic. The uniform boundedness principle states that a pointwise bounded family of continuous linear operators between Banach spaces is equicontinuous.
Numerology
Chaldean Numerology
The numerical value of equicontinuity in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of equicontinuity in Pythagorean Numerology is: 4
Translations for equicontinuity
From our Multilingual Translation Dictionary
- ligekontinuitetDanish
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"equicontinuity." Definitions.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.definitions.net/definition/equicontinuity>.
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