In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right" definitions in order to make this work. In this mini PSP, we work through Frechet's entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet's newly coined term, are compact.
Applicable Math Courses
Upper Division Undergraduate
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Scoville, Nicholas A., "A Compact Introduction to a Generalized Extreme Value Theorem" (2017). Topology. 5.