Genus and the Lyusternik-Schnirelmann category of preimages
Abstract
In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik - Schnirelmann category is considered. For this function and a given map of the underlying space to a finite polyhedron some lower bounds on the value of this function on the preimage of some point are given.
References
1. Lusternik L.A., Schnirelmann L.G. Methodes topologiques dans le probiemes variationnels. - Paris: Hermann, 1934.
2. Berstein I., Ganea T. The category of a map and of a cohomology class // Fundam. Math. - 1961. - 50. - P. 265-279.
3. James I.M. On category, in the sense of Lusternik - Schnirelmann // Topology. - 1978. - 17. - P. 331-348.
4. Schwarz A.S. The genus of a fibre space // Amer. Math. Soc. Transl. - 1966 .- 55. - P. 49-140.
5. Yang C.-T. On Theorems of Borsuk - Ulam, Kakutani - Yamabe - Yujobo and Dyson, II // The Annals of Mathematics. - 1955. - 2nd Ser. - 62(2). - P. 271-283.
6. Воловиков А.Ю. Точки совпадения отображений -пространств // Изв. РАН.: Сер. матем. - 2005. - 69(5) - С. 53-106.
7. Varadarajan K. On fibrations and category // Mathematische Zeitschrift. - 1965. - 88. - P. 267-273.
8. Krasnosel'skii M.A. On special coverings of a finite-dimensional sphere// Dokl. Akad. Nauk SSSR. - 1955. - 103. - P. 961-964.
9. Yang C.-T. Continuous Functions From Spheres to Euclidean Spaces // The Annals of Mathematics. - 1955. - 2nd Ser. - 62(2). - P. 284-292.
10. Froloff S., Elsholz L. Limite inferieure pour le nombre des valeurs critiques d'une fonction, donne sur une variete // Math. Sbornik. - 1935. - 42(5). - P. 637-643.
Review
For citations:
Karasev R.N. Genus and the Lyusternik-Schnirelmann category of preimages. Modeling and Analysis of Information Systems. 2007;14(4):31-35. (In Russ.)
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