Historique de la notion de compacite

@article{Pier1980HistoriqueDL,
  title={Historique de la notion de compacite},
  author={Jean-Paul Pier},
  journal={Historia Mathematica},
  year={1980},
  volume={7},
  pages={425-443}
}
Abstract The Bolzano-Weierstrass and Borel-Lebesgue properties of sets constitute the fundamental ideas that led to the notion of compactness. The link between these ideas appeared for the first time to Frechet, who formulated the first definition of a compact set. The notion developed simultaneously with that of a complete set thanks mainly to the contributions made by Hausdorff and Alexandroff. Later Moore-Smith convergence and filters enabled simplification of the language. 
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References

SHOWING 1-10 OF 25 REFERENCES
On the foundations of the calcul fonctionnel of Fréchet
In his thesis, t Frechet gave a very beautiful generalization of the theory of point sets and of the theory of real valued functions of a real variable. His functions are real valued but the range ofExpand
On the equivalence of Écart and voisinage
1. Frechet has suggested that being given a class (V) for which a "voisinage " is defined it should be possible to give a definition of " 6cart" in this class such that the convergent sequences andExpand
Sur les ensembles abstraits
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1921, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.Expand
A General Theory of Limits
I. As to Notions.-In this paper we investigate a simple general limit of which, as will appear in ? 5, the various classical limits of analysis are actually instances.* The general limit in questionExpand
Éléments d'histoire des mathématiques
Ce volume rassemble les notes historiques parues dans les differentslivres des elements de mathematique de l'auteur. Ellesconcernent donc l'ensemble des matieres abordees dans ce traite: theorie desExpand
Genèse et évolution de l'idée de compact.
Pier Jean-Paul. Genese et evolution de l'idee de compact.. In: Revue d'histoire des sciences et de leurs applications, tome 14, n°2, 1961. pp. 169-179.
Ueber trigonometrische Reihen.
§. 1. JJis in die neueste Zeit glaubte man, es sei das Integral einer convergenten Reihe, deren Glieder zwischen endlichen Integrationsgrenzen endlich bleiben, gleich der Summe aus den Integralen derExpand
Relations entre les notions de limite et de distance
1. Un certain nombre de proprietes des ensembles lineaires peuvent etre etendues aux ens'embles abstraits, c'est a dire aux ensembles dont les elements sont de nature quelconque ou inconnue. C'estExpand
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