PlanetMath: closed graph theorem

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closed graph theorem

(Theorem)

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

"closed graph theorem" is owned by Koro.

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Cross-references: product topology, closed subset, continuous, Banach spaces, linear mapping
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This is version 5 of closed graph theorem, born on 2002-12-09, modified 2006-07-27.
Object id is 3702, canonical name is ClosedGraphTheorem.
Accessed 5235 times total.

Classification:

46A30 (Functional analysis :: Topological linear spaces and related structures :: Open mapping and closed graph theorems; completeness )

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