A Pedagogical History of Compactness

@article{RamanSundstrm2015APH,
  title={A Pedagogical History of Compactness},
  author={Manya Raman-Sundstr{\"o}m},
  journal={The American Mathematical Monthly},
  year={2015},
  volume={122},
  pages={619 - 635}
}
Abstract This paper traces the history of compactness from the original motivating questions through the development of the definition to a characterization of compactness in terms of nets and filters. The goal of the article is to clarify the central concepts of open-cover and sequential compactness, including details that a standard textbook treatment tends to leave out. 
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Topics from this paper

Introduction to Metric and Normed Spaces
Differentiation and Integration
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Measure on the Real Line
The Open Limit Point Compactness
Open texture clarified
Set Theory and Numbers
Partial data querying through racing algorithms
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