La compacitat, una noció seminal en l'evolució de la topologia general (1895-1930)

Authors

  • Júlia Moreno Montes
  • Mónica Blanco Abellán
  • Pere Pascual Gainza

Abstract

In this paper we analyze the evolution of the notion of compactness for topological spaces from its first appearance in a Fréchet 1904 paper generalising the Bolzano-Weierstrass property, encompassing its relationship with the Borel covering theorem for the interval [0, 1], and including the general definition based on the Heine-Borel property for arbitrary open covers in 1929. We focus our analysis on four key works: Borel's thesis, Fréchet's thesis, Hausdorff's Grundzüge and Alexandroff-Urysohn's memoire.

Downloads

Published

2020-09-08

How to Cite

Moreno Montes, J., Blanco Abellán, M., & Pascual Gainza, P. (2020). La compacitat, una noció seminal en l’evolució de la topologia general (1895-1930). Butlletí De La Societat Catalana De Matemàtiques, 35(1), 23–56. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/107697.003

Issue

Vol. 35 No. 1 (2020)

Section

Articles

License

The intellectual property of articles belongs to the respective authors.

On submitting articles for publication to the journal Butlletí de la Societat Catalana de Matemàtiques, authors accept the following terms:

  1. Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Butlletí de la Societat Catalana de Matemàtiques.
  2. Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.
  3. Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.
  4. Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.
  5. The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.
  6. The journal Butlletí de la Societat Catalana de Matemàtiques is not responsible for the ideas and opinions expressed by the authors of the published articles.