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单词 ExtremePoint
释义

extreme point


Definition.

Let C be a convex subset of a vector space X. A point xC iscalled an extreme pointPlanetmathPlanetmath if it is not an interior point of any line segmentMathworldPlanetmathin C. That is x is extreme if and only if whenever x=ty+(1-t)z, t(0,1), zy, implies either yC or zC.

For example the set [0,1] is a convex set and 0 and 1 are the extreme points.

References

  • 1 H. L. Royden. . Prentice-Hall, Englewood Cliffs, New Jersey, 1988
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