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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On homological situation properties of complexes and closed sets
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by Paul Alexandroff PDF
Trans. Amer. Math. Soc. 54 (1943), 286-339 Request permission
References
  • Paul Alexandroff, General combinatorial topology, Trans. Amer. Math. Soc. 49 (1941), 41–105. MR 4125, DOI 10.1090/S0002-9947-1941-0004125-1
    • —, (a) Homologiegruppen allgemeiner Projectionsspectra; (b) Allgemeiner Dualitätssatz für Projectionsspectra und für im Kleinen bikompakte Räume, Mitteilungen der Georgischen Abteilung der Akademie der Wissenschaften der SSR vol. 2 (1941) pp. 213-219 and 315-319 (in Russian with a German summary).
  • P. Alexandroff, Zurückführung des Alexander-Pontrjaginschen Dualitätssatzes auf den Dualitätssatz von Kolmogoroff, Mitt. Georg. Abt. Akad. Wiss. USSR [Soobščenia Gruzinskogo Filiala Akad. Nauk SSSR] 1 (1940), 401–410 (Russian, with German summary). MR 0004768
    • P. Alexandroff and H. Hopf, Topologie, I, 1935.
  • P. Alexandroff, H. Hopf, and L. Pontrjagin, Über den Brouwerschen Dimensionsbegriff, Compositio Math. 4 (1937), 239–255 (German). MR 1556970
  • M. Bockstein, Über die Homologiegruppen der Vereinigung zweier Komplexe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 365–376 (German, with Russian summary). MR 0004782
  • Hans Freudenthal, Zum Hopfschen Umkehrhomomorphismus, Ann. of Math. (2) 38 (1937), no. 4, 847–853 (German). MR 1503376, DOI 10.2307/1968841
    • A. Kolmogoroff, Über die Dualität im Aufbau der kombinatorischen Topologie, Rec. Math. (Mat. Sbornik) N.S. vol. 1 (1936) pp. 97-102. S. Lefschetz, On closed sets on a manifold, Ann. of Math. (2) vol. 29 (1928) pp. 232-254. L. Pontrjagin, Topological groups. —, Zum Alexanderschen Dualitätssatz. II, Nachr. Ges. Wiss. Göttingen, 1927, pp. 446-454. Seifert-Threlfall, Topologie, 1934.
  • Norman E. Steenrod, Universal Homology Groups, Amer. J. Math. 58 (1936), no. 4, 661–701. MR 1507191, DOI 10.2307/2371239
  • A. W. Tucker, An abstract approach to manifolds, Ann. of Math. (2) 34 (1933), no. 2, 191–243. MR 1503105, DOI 10.2307/1968201
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Additional Information
  • © Copyright 1943 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 54 (1943), 286-339
  • MSC: Primary 56.0X
  • DOI: https://doi.org/10.1090/S0002-9947-1943-0008700-1
  • MathSciNet review: 0008700