Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On ordinally closed sets
HTML articles powered by AMS MathViewer

by John C. Morgan PDF
Proc. Amer. Math. Soc. 68 (1978), 92-96 Request permission

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
    R. Baire, Sur les fonctions de variables réelles, Ann. Mat. Pura Appl. (3) 3 (1899), 1-123.
  • 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
  • Arnaud Denjoy, L’Énumération Transfinie. Livre I. La Notion de Rang, Gauthier-Villars, Paris, 1946 (French). MR 0018190
  • I. Grattan-Guinness, The correspondence between Georg Cantor and Philip Jourdain. 1, Jber. Deutsch. Math.-Verein. 73 (1971/72), no. part, 111–130. MR 490811
  • John C. Morgan II, Infinite games and singular sets, Colloq. Math. 29 (1974), 7–17, 159. MR 351821, DOI 10.4064/cm-29-1-7-17
  • F. Riesz, Stetigkeitsbegriff und abstrakte Mengenlehre, Atti IV Congr. Internaz. Mat., Roma, 1908, Vol. II, pp. 18-24. W. Sierpiński, Uogólnienie pewnego twierdzenia Cantora z teorji mnogości punktowych, Wektor 4 (1915), 49-51. —, 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.) —, Sur un ensemble linéaire non dénombrable qui est de première catégorie sur tout ensemble parfait, C. R. Soc. Sci. Varsovie 25 (1932), 102-105. —, Sur l’existence des suites transfinies décroissantes d’ensembles ${F_\sigma }$, C. R. Soc. Sci. Varsovie 26 (1933), 85-89. W. H. and G. C. Young, The theory of sets of points, Chelsea, New York, 1972. 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
  • © Copyright 1978 American Mathematical Society
  • 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