---- > [!definition] Definition. ([[closed linear operator]]) > A [[linear operator]] $T$ between [[topological vector space|topological vector spaces]] $V$ and $W$ is said to be **closed** if its [[graph]] is [[closed set|closed]] as a subset of $V \times W$ equipped with the [[product topology]]. > By the [[closed graph theorem]], this notion is equivalent to [[continuous|continuity]] when $V,W$ are nice enough (e.g. [[Banach space|Banach]]). ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```