Functional analysis: Difference between revisions

Revision as of 23:45, 16 October 2022

Revision as of 23:47, 16 October 2022

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{{main|Closed graph theorem}}

The closed graph theorem states the following:

If ''<math>X''</math> is a [[topological space]] and ''<math>Y''</math> is a [[Compact space|compact]] [[Hausdorff space]], then the graph of a linear map ''<math>T''</math> from ''<math>X''</math> to ''<math>Y''</math> is closed if and only if ''<math>T''</math> is [[continuous function (topology)|continuous]].<ref>{{Cite book|last=Munkres|first=James R.|url={{google books |plainurl=y |id=XjoZAQAAIAAJ}}|title=Topology|date=2000|publisher=Prentice Hall, Incorporated|isbn=978-0-13-181629-9|language=en| page= 171}}</ref>

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