The roots of the emergence of the notion of compactness and the history of compression theory

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur, Iran

Abstract

Given the significant impact of the concept of compactness in advanced mathematics and the importance of a correct and appropriate understanding of this concept for entering modern mathematics, it seems necessary and useful to study its roots, the beginning of its formation, and its development path. In this article, we first examine the roots of the emergence of the concept of compactness. Then, we explore the crucial impact and the key to the possibility of moving from an arbitrary open cover to a finite subcover in the proof of an important modern analysis theorem to make the philosophy behind the definition of compactness more apparent. Finally, we review the history of compression theory with a focus on pointwise compression and the Stone-Čech compression.

Keywords

References

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Mathematics and Society
Volume 3, Issue 4 - Serial Number 4
December 2018
Pages 13-24

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History

  • Receive Date: 29 May 2018
  • Revise Date: 09 December 2018
  • Accept Date: 12 December 2018
  • Publish Date: 20 February 2019

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