Editing Plateau (mathematics)

A '''plateau''' of a [[function (mathematics)|function]] is a part of its [[domain of a function|domain]] where the function has constant value.

More formally, let ''U'', ''V'' be [[topological space]]s. A '''plateau''' for a  function ''f'': ''U'' → ''V'' is a [[path-connected]] set of points ''P'' of ''U'' such that for some ''y'' we have
:''f''&nbsp;(''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. 
<ref name="SahneyBenton2008">{{cite journal | url= |author1=Sahney, S.  |author2=Benton, M.J.  |name-list-style=amp | year=2008 | title=Recovery from the most profound mass extinction of all time | journal=Proceedings of the Royal Society B: Biological Sciences | doi=10.1098/rspb.2007.1370 | volume = 275 | pages = 759–65| pmid=18198148 | issue=1636 | pmc=2596898}}</ref>

==See also==
*[[Level set]]
*[[Contour line]]
*[[Minimal surface]]

==References==
{{Reflist}}
{{PlanetMath attribution|id=3374|title=plateau}}

[[Category:Topology]]


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