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plateau (Definition)

A plateau of a function is a region where a function has constant value.

More formally, let $ U$ and $ V$ be topological spaces. A plateau for a scalar function $ f: U \to V$ is a path-connected set of points $ P \subseteq U$ such that for some $ y$ we have

$\displaystyle \forall p \in P, f(p) = y$ (1)

Please take note that this entry is not authoritative. If you know of a more standard definition of “plateau”, please contribute it, thank you.



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"plateau" is owned by bshanks. [ full author list (2) ]
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See Also: extremum

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Cross-references: points, path-connected, scalar, topological spaces, region, function
There are 2 references to this entry.

This is version 5 of plateau, born on 2002-08-28, modified 2005-03-29.
Object id is 3374, canonical name is Plateau.
Accessed 3386 times total.

Classification:
AMS MSC26B12 (Real functions :: Functions of several variables :: Calculus of vector functions)
 90-00 (Operations research, mathematical programming :: General reference works )

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