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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, Naveen Somasunderam
Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, Naveen Somasunderam
Analysis
No abstract provided.
A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville
A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville
Topology
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.