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Reference.org
Closed graph theorem
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the closed graph theorem may refer to one of several basic results characterizing <a href="/facts/Continuous_function/sKbl02pB">continuous functions</a> in terms of their <a href="/facts/Graph_of_a_function/htYX0BGX">graphs</a>. Each gives conditions when functions with <a href="/facts/Closed_graph/canolygI">closed graphs</a> are necessarily continuous. </p><p>A blog post by <a href="/facts/Terence_Tao/Do68JKn6">T. Tao</a> lists several closed graph theorems throughout mathematics. </p>