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An Analysis of the First Proofs of the Heine-Borel Theorem - Works Cited

Author(s): 
Nicole R. Andre (Wittenberg University), Susannah M. Engdahl (Wittenberg University), and Adam E. Parker (Wittenberg University)

Works Cited

1. Bloch, E. (2011). The real numbers and real analysis. New York: Springer.

2. Borel, É. (1903). Contribution à l’analyse arithmétique du continu. Journal de mathématiques pures et appliquées 5e série, 329-375.

3. Borel, É. (1898). Leçons sur la théorie des fonctions. Paris: Gauthier-Villars.

http://www.archive.org/details/leconstheoriefon00borerich

4. Borel, É. (1903). Sur l'approximation des nombres par des nombres rationnels. Comptes Rendus de l'Académie des Sciences de Paris, 1054-1055.

5. Borel, É. (1895). Sur quelques points de la théorie des fonctions. Annales scientifiques de l'E.N.S. Serie 3, 12, 9-55.

http://www.numdam.org/item?id-ASENS_1895_3_12__9_0

6. Bressoud, D. M. (2008). A radical approach to Lebesgue's theory of integration. New York: Cambridge University Press.

7. Cousin, P. (1895). Sur les fonctions de n variables complexes. Acta Mathematica, 19, 22.

http://dx.doi.org/10.1007/BF02402869

8. Dugac, P. (1989). Sur la correspondance de Borel et le théorème de Dirichlet-Heine-Weierestrass-Borel-Schoenflies-Lebesgue. Archives internationales d'histoire des sciences, 39 (122), 69-110.

9. Hallett, M. (1979). Towards a theory of mathematical research programmes (I). The British Journal for the Philosophy of Science, 30 (1), 1-25.

10. Hawkins, T. (1980). The origins of modern theories of integration. In I. Grattan-Guinness, From the calculus to set theory 1630-1910, an introductory history (p. 175). Princeton: Princeton University Press.

11. Hildebrandt, T. (1926). The Borel theorem and its generalizations. Bulletin of the American Mathematical Society, 423-425.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183487130

12. Koetsier, T. and J. van Mill (1999). By their fruits ye shall know them: some remarks on the interaction of general topology with other areas of mathematics. In History of Topology (pp. 199-239). Amsterdam: North-Holland Publishing Company.

13. Lebesgue, H. (1907). Comptes rendus et analyses: Review of Young and Young, The theory of sets of points. Bulletin des sciences mathématiques (2), 31, 132-134.

14. Lebesgue, H. (1904). Leçons sur l'intégration et la recherche des fonctions primitives. Paris.
http://ia600201.us.archive.org/23/items/leconegrarecher00leberich/leconegrarecher00leberich.pdf

15. Schoenflies, A. (1900). Die Entwickelung der Lehre von den Punktmannigfaltigkeiten. In Jahresbericht der deutschen Mathematiker-Vereinigung. Leipzig: B.G. Teubner. Also available from Google Books.

16. Schoenflies, A. (1907). Sur un théorème de Heine et un théorème de Borel. Comptes Rendus de l'Académie des Sciences de Paris, 144, 22-23.

http://gallica.bnf.fr/ark:/12148/bpt6k3098j/f22.tableDesMatieres

17. Stoll, R. R. (1979). Set Theory and Logic. New York, New York, USA: Dover.

18. Sundström, M. R. (2010 21-June). A pedagogical history of compactness.
From arxiv: http://arxiv.org/abs/1006.4131

19. Young, W. H. (1902). Overlapping intervals. Bulletin of the London Mathematical Society, 35, 384-388.

http://plms.oxfordjournals.org/content/s1-35/1/384.full.pdf

Dummy View - NOT TO BE DELETED