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File:Unit square ɛ-net.svg

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Description
English: An example of an ɛ-net in the computational geometry sense. In this example, the range space (X, R) has X equal to the set of points in the 2D plane, and R equal to the set of closed filled rectangles (products of closed intervals). The set P shown is the unit square, and the 8 points shown are an ɛ-net of this square with ɛ=1/4, since no closed filled rectangle can intersect at least 1/4 of the square without also intersecting one of these 8 points. Note that any axis-parallel square regardless of size would have a similar 1/4-net of 8 points.
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Source Own work
Author Dcoetzee

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28 June 2010

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Date/TimeThumbnailDimensionsUserComment
current01:35, 29 June 2010Thumbnail for version as of 01:35, 29 June 2010291 × 308 (14 KB)Dcoetzee{{Information |Description={{en|1=An example of an ɛ-net in the computational geometry sense. In this example, the range space (X, R) has X equal to the set of points in the 2D plane, and R equal to the set of closed filled rectangles (products of closed

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