A plateau of a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-orie ...
is a part of its
domain
A domain is a geographic area controlled by a single person or organization. Domain may also refer to:
Law and human geography
* Demesne, in English common law and other Medieval European contexts, lands directly managed by their holder rather ...
where the function has constant value.
More formally, let ''U'', ''V'' be
topological space
In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a to ...
s. A plateau for a function ''f'': ''U'' → ''V'' is a
path-connected
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties t ...
set of points ''P'' of ''U'' such that for some ''y'' we have
:''f'' (''p'') = ''y''
for all ''p'' in ''P''.
Examples
Plateaus can be observed in mathematical models as well as natural systems. In nature, plateaus can be observed in physical, chemical and biological systems. An example of an observed plateau in the natural world is in the tabulation of biodiversity of life through time.
See also
*
Level set
In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is:
: L_c(f) = \left\~.
When the number of independent variables is two, a level set is call ...
*
Contour line
A contour line (also isoline, isopleth, isoquant or isarithm) of a Function of several real variables, function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a ...
*
Minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below).
The term "minimal surface" is used because these surfaces originally arose as surfaces that ...
References
Topology
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