Editing Closed graph theorem (section)

{{Short description|Theorem relating continuity to graphs}}
{{About|closed graph theorems in [[general topology]]|the closed graph theorem in [[functional analysis]]|Closed graph theorem (functional analysis)}}
{{multiple image
| footer = The graph of the [[cubic function]] <math>f(x) = x^3 - 9x</math> on the interval <math>[-4, 4]</math> is closed because the function is [[Continuous function|continuous]]. The graph of the [[Heaviside function]] on <math>[-2, 2]</math> is not closed, because the function is not continuous.
| width     = 200
| image1    = cubicpoly.png
| alt1      = A cubic function
| image2    = Dirac distribution CDF.svg
| alt2      = The Heaviside function
}}
In [[mathematics]], the '''closed graph theorem''' may refer to one of several basic results characterizing [[continuous function]]s in terms of their [[graph of a function|graph]]s. 
Each gives conditions when functions with [[closed graph]]s are necessarily continuous.

A blog post<ref name="Tao">{{cite web | url=https://terrytao.wordpress.com/2012/11/20/the-closed-graph-theorem-in-various-categories/ | title=The closed graph theorem in various categories | date=21 November 2012 }}</ref> by [[Terence Tao|T. Tao]] lists several closed graph theorems throughout mathematics.