Functional analysis
Closed graph theorem

Closed graph theorem — If X {\displaystyle X} is a topological space and Y {\displaystyle Y} is a compact Hausdorff space, then the graph of a linear map T {\displaystyle T} from X {\displaystyle X} to Y {\displaystyle Y} is closed if and only if T {\displaystyle T} is continuous.
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