Editing Closed graph theorem (section)

=== For set-valued functions ===

{{Math theorem
| name = Closed graph theorem for set-valued functions<ref name="aliprantis">{{cite book|title=Infinite Dimensional Analysis: A Hitchhiker's Guide|last=Aliprantis|first=Charlambos|author2=[[Kim C. Border]]|publisher=Springer|year=1999|edition=3rd|chapter=Chapter 17}}</ref>
| math_statement = For a [[Hausdorff space|Hausdorff]] [[Compact space|compact]] range space <math>Y</math>, a set-valued function <math>F : X \to 2^Y</math> has a closed graph if and only if it is [[upper hemicontinuous]] and {{math|''F''(''x'')}} is a closed set for all <math>x \in X</math>.
}}