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State and Prove closed Graph Theorem. |
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Answer» Inmathematics, theclosed graph theoremis a basic result which characterizescontinuous functionsin terms of theirgraphs. There are several versions of the theorem. The closed graph theoremIn point-set topology For any functionT:X→Y, we define thegraphofTto be the set Inpoint-set topology, the closed graph theorem states the following: IfXis atopological spaceandYis acompactHausdorff space, then the graph ofTis closed if and only ifTiscontinuous. Msc paper |
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