| 单词 |
pointwise |
| 释义 |
ˈpointwise, adv.
[f. point n.1 B. + -wise.]
1. In the manner or way of a point.
1545Elyot, Cuspidatim, poyntyng, or poyntwyse. 1611Florio, Stipula, the spindling vp point-wise of any thing namely of corne. 1616J. Lane Cont. Sqr.'s T. ix. 197 Gnartolite..whome Akafir, well eienge, point wise smote. 1904Westm. Gaz. 25 Feb. 4/1 The bodice..enriched with further appliqués of guipure to extend the fronts pointwise.
2. Math. With regard to individual points; esp. in pointwise convergent, that converges for each individual point in a space, but not necessarily for the space as a whole (so pointwise convergence).
1932Colloquium Publ. Amer. Math. Soc. XV. i. 26 The term ‘convergence in the mean’ was introduced to distinguish convergence in the space 𝔏2..from ordinary point-wise convergence. 1955Hall & Spencer Elem. Topology iv. 133 This sequence is said to converge point⁓wise to a mapping f:S → T, if and only if, for each point x of S, the sequence {ob}fn(x){cb} of points of T converges to the point f(x) of T. 1966A. Feinstein tr. G. Choquet's Topology i. 92 Every sequence (fn) which converges uniformly to f converges pointwise to f, but it is important to note that the converse is incorrect. 1970Manifold VI. 17 A student produced three new specimens... They came from adding the blackboard examples point⁓wise. 1971Powell & Higman Finite Simple Groups iii. 138 And r leaves a hyperplane pointwise fixed. 1974G. J. O. Jameson Topology & Normed Spaces ix. 90 A decreasing sequence of continuous functions on a compact space can certainly be pointwise convergent to a discontinuous function. |
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