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Extreme Point


An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes denoted E(K).

Extreme points play important roles in a number of areas of mathematics, e.g., in the Krein-Milman theorem which says that, despite their moniker implying a certain degree of rarity, the collection E(K) can be quite large relative the host space X.


See also

Extreme Set, Krein-Milman Theorem

This entry contributed by Christopher Stover

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References

Rudin, W. Functional Analysis. New York: McGraw-Hill, 1991.

Cite this as:

Stover, Christopher. "Extreme Point." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ExtremePoint.html

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