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pointwise

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pointwise 数学

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英语
This theorem is important, since pointwise convergence of continuous functions is not enough to guarantee continuity of the limit function as the image illustrates.
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It is not clear "a priori" whether the series converges pointwise.
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The addition operation is defined by pointwise addition of functions and the multiplication operation is defined by function composition.
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However, it can be shown that concatenation and pointwise multiplication are homotopic.
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In a pointwise estimator, the kernel width is varied depending on the location of the sample.
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The pointwise limit of a sequence of continuous functions may be a discontinuous function, but only if the convergence is not uniform.
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As functions, pointwise larger t-norms are sometimes called "stronger" than those pointwise smaller.
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The construction of discontinuous functions fails because a function is identified with a curve, and the curve can not be constructed pointwise.
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Pointwise orders also inherit some properties of the underlying posets.
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Operations from are interpreted on the reduced product by applying the operation pointwise.
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