# closed graph theorem

A linear mapping between two Banach spaces $X$ and $Y$ is continuous if and only if its graph (http://planetmath.org/Graph2) is a closed subset of $X\times Y$ (with the product topology).

Title closed graph theorem ClosedGraphTheorem 2013-03-22 13:13:56 2013-03-22 13:13:56 Koro (127) Koro (127) 8 Koro (127) Theorem msc 46A30 OpenMappingTheorem Graph2