Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On ordinally closed sets


Author: John C. Morgan
Journal: Proc. Amer. Math. Soc. 68 (1978), 92-96
MSC: Primary 04A15
DOI: https://doi.org/10.1090/S0002-9939-1978-0457217-8
MathSciNet review: 0457217
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Extensions of Cantor's Intersection Theorem and Zalcwasser's theorem on transfinite sequences of ambiguous sets of the first Baire class are given for linear sets.


References [Enhancements On Off] (What's this?)

  • [1] R. Baire, Sur les fonctions de variables réelles, Ann. Mat. Pura Appl. (3) 3 (1899), 1-123.
  • [2] Georg Cantor, Contributions to the founding of the theory of transfinite numbers, Dover Publications, Inc., New York, N. Y., 1952. Translated, and provided with an introduction and notes, by Philip E. B. Jourdain. MR 0045635
  • [3] Arnaud Denjoy, L’Énumération Transfinie. Livre I. La Notion de Rang, Gauthier-Villars, Paris, 1946 (French). MR 0018190
  • [4] I. Grattan-Guinness, The correspondence between Georg Cantor and Philip Jourdain. part 1, Jber. Deutsch. Math.-Verein. 73 (1971/72), no. part 1, 111–130. MR 0490811
  • [5] John C. Morgan II, Infinite games and singular sets, Colloq. Math. 29 (1974), 7–17, 159. MR 0351821
  • [6] F. Riesz, Stetigkeitsbegriff und abstrakte Mengenlehre, Atti IV Congr. Internaz. Mat., Roma, 1908, Vol. II, pp. 18-24.
  • [7] W. Sierpiński, Uogólnienie pewnego twierdzenia Cantora z teorji mnogości punktowych, Wektor 4 (1915), 49-51.
  • [8] -, Un théorème sur les ensembles fermés, Bull. Sci. Math. (2) 41 (1917), 290-292 (also appeared in Bull. Intern. Acad. Sci. Cracovie,1918, 49-51.)
  • [9] -, Sur un ensemble linéaire non dénombrable qui est de première catégorie sur tout ensemble parfait, C. R. Soc. Sci. Varsovie 25 (1932), 102-105.
  • [10] -, Sur l'existence des suites transfinies décroissantes d'ensembles $ {F_\sigma }$, C. R. Soc. Sci. Varsovie 26 (1933), 85-89.
  • [11] W. H. and G. C. Young, The theory of sets of points, Chelsea, New York, 1972.
  • [12] Z. Zalcwasser, Un théorème sur les ensembles qui sont à la fois $ {F_\sigma }$ et $ {G_\delta }$, Fund. Math. 3 (1922), 44-45.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04A15

Retrieve articles in all journals with MSC: 04A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0457217-8
Keywords: Cantor's Intersection Theorem, ordinally closed sets, stationary sequences of sets, monotone family of sets
Article copyright: © Copyright 1978 American Mathematical Society