| 单词 | ε-net |
| 释义 | > as lemmasε-net 6. Mathematics. A mapping from an ordered set into a topological space; the sequence of points in the space which is the domain of such a mapping; spec. (in full ε-net) a sequence of points in a topological space such that every point of the space lies within a (usually small) distance ε of a point in the sequence. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > into or from a space path1912 vector field1922 scalar field1932 net1939 1939 M. H. A. Newman Elem. Topol. Plane Sets Points ii. 39 An ε-net in E is a finite set of points, A, such that every point of E is within a distance ε of at least one point of A. 1959 G. James & R. C. James Math. Dict. (ed. 2) 260/1 A net..of a set S is a mapping of a directed set into S. 1968 E. T. Copson Metric Spaces vi. 76 A sequentially compact metric space possesses an ε-net for every positive value of ε. 1968 E. T. Copson Metric Spaces vi. 77 Let An be a set of points in the totally bounded metric space M which forms a 1/n-net. 1993 Internat. Jrnl. Control 58 666 Approximation properties of totally bounded (relatively compact) sets, the n-width and ε-net concepts all have a considerable role to play in the present work. < as lemmas |
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