Given a barrelled space " X " and a locally convex space " Y ", then any family of pointwise bounded continuous linear mappings from " X " to " Y " is equicontinuous ( even uniformly equicontinuous ).
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For example, if the sequence consists of differentiable functions or functions with some regularity ( e . g ., the functions are solutions of a differential equation ), then the mean value theorem or some other kinds of estimates can be used to show the sequence is equicontinuous.
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Equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of " C " ( " X " ), the space of continuous functions on a compact Hausdorff space " X ", is compact if and only if it is closed, pointwise bounded and equicontinuous.
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*When is Cauchy's formula ) its derivative has modulus bounded by } } in the smaller disk " B " ( " z " 0, ) . } } If a family of holomorphic functions on is bounded by on, it follows that the family of restrictions to is equicontinuous on.
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:: : OK, then the topology should be the topology of uniform convergence; but in fact on equicontinuous families it coincides with the topology of pointwise convergence ( the one induced by the product topology; incidentally, this fact yields to a proof of AA theorem, via Tychonoff's theorem )-- a 22 : 23, 21 May 2012 ( UTC)
How to say equicontinuous in Hindi and what is the meaning of equicontinuous in Hindi? equicontinuous Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
