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. 
View on Taylor & Francis
umu.diva-portal.org
14 Citations

Topics from this paper

      14 Citations

      Citation Type

      Citation Type

      Simple way to prove compactness of closed intervals in simply ordered set with order topology
      Introduction to Metric and Normed Spaces
      Differentiation and Integration
      General Measure Spaces
      Measure on the Real Line
      The Open Limit Point Compactness
      Compactness on Soft Topological Ordered Spaces and Its Application on the Information System
      Open texture clarified
      Set Theory and Numbers
      Partial data querying through racing algorithms
      ...
      1
      2
      ...

      References

      SHOWING 1-10 OF 57 REFERENCES
      E.W. Chittenden and the early history of general topology
      The Rôle of Compactness in Analysis
      Historique de la notion de compacite
      The establishment of functional analysis
      Handbook of the History of General Topology
      By their fruits ye shall know them: some remarks on the interaction of general topology with other areas of mathematics
      The emergence of open sets, closed sets, and limit points in analysis and topology
      History of functional analysis
      The Mathematical Works of Bernard Bolzano
      Algebraic Geometry
      ...
      1
      2
      3
      4
      5
      ...