Pacific Journal of Mathematics

Some abstract generalizations of the Ljusternik-Schnirelmann-Borsuk covering theorem.

H. Steinlein

Article information

Source
Pacific J. Math., Volume 83, Number 1 (1979), 285-296.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102784677

Mathematical Reviews number (MathSciNet)
MR555055

Zentralblatt MATH identifier
0413.55002

Subjects
Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space

Citation

Steinlein, H. Some abstract generalizations of the Ljusternik-Schnirelmann-Borsuk covering theorem. Pacific J. Math. 83 (1979), no. 1, 285--296. https://projecteuclid.org/euclid.pjm/1102784677


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References

  • [1] K. Borsuk, Dre Sdtze uber die n-dimensionaleeuklidische Sphdre, Fund. Math., 20 (1933), 177-190.
  • [2] J. Dugundji, A duality property of nerves, Fund. Math., 59 (1966), 213-219.
  • [3] Sze-Tsen Hu, Homotopy Theory, Academic Press, New York and London, 1959.
  • [4] M. A. Krasnoseski, On special coverings of a finite-dimensional sphere, Doklady Akad. Nauk SSSR, 103 (1955), 961-964. (Russian)
  • [5] L. Ljusternik and L. Schnirelmann, Topological methods in variationalproblems,
  • [6] A. S. Svarc, Some estimates of the genus of a topologcal space in the sense of Krasnoseski, Uspehi Mat. Nauk, 12 (1957), no. 4 (76), 209-214. (Russian)
  • [7] A. S. Svarc,The genus of a fiber space, Trudy Moskov. Mat. Obsc., 10 (1961), 217-272 and 11 (1962), 99-126; (Russian), English translation in Amer. Math. Soc, Translat., II. Ser., 55 (1966), 49-140.
  • [8] H. Steinlein, Borsuk-Ulam Sdtze und Abbildungen mit kompakten Iterierten, Habili- tationsschrift, University of Munich, 1976.
  • [9] Chung-Tao Yang, On theorems of Borsuk-Ulam,Kakutani-Yamabe-Yujoboand Dyson, I, Ann. Math., 60 (1954), 262-282.