An application of the Stiefel-Whitney classes to the proof of a fixed point theorem for set-valued mappings

• Autorzy: Miklaszewski D.

Identyfikatory

DOI

10.4064/ba53-2-7

• Języki publikacji: EN

Abstrakty

EN

We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.

Słowa kluczowe

EN

fixed points of set-valued mappings; Stiefel-Whitney classes; Borsuk continuity

PL

punkty stałe odwzorowań zbiór-wartość; klasa Stiefela-Whitney'a; ciągłość Borsuka

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 2
• Strony: 181--186
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Miklaszewski D.

• Faculty of Mathematics and Computer Science, Nicholaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland,

Bibliografia

• [1] K. Borsuk, On some metrization of the hyperspace of compact sets, Fund. Math. 41 (1954), 168-202.
• [2] T. A. Chapman and S. Ferry, Approximating homotopy equivalences by homéomorphisme, Amer. J. Math. 101 (1979), 583-607.
• [3] F. Cohen, Cohomology of braid spaces, Bull. Amer. Math. Soc. 79 (1973), 763-766.
• [4] E. Dyer and М. E. Hamstrom, Completely regular mappings, Fund. Math. 45 (1957), 103-118.
• [5] S. Ferry, Homotoping ϵ-maps to homeomorphisms, Amer. J. Math. 101 (1979), 567¬582.
• [6] L. Górniewicz, Present state of the Brouwer fixed point theorem for multivalued mappings, Ann. Sci. Math. Québec 22 (1998), 169-179.
• [7] D. Husemoller, Fibre Bundles, McGraw-Hill, 1966.
• [8] W. Jakobsche, Approximating homotopy equivalences of surfaces by homéomorphisme, Fund. Math. 118 (1983), 1-9.
• [9] —, Approximating homotopy equivalences of 3-manifolds by homeomorphisms, ibid. 130 (1988), 157-168.
• [10] J. P. May, Homology operations on infinite loop spaces, in: Algebraic Topology, Proc. Sympos. Pure Math. 12, Amer. Math. Soc., 1971, 171-186.
• [11] D. Miklaszewski, On the Brouwer fixed point theorem, Topology Appl. 119 (2002), 53-64.
• [12] —, A fixed point theorem for multivalued mappings with nonacyclic values, Topol. Methods Nonlinear Anal. 17 (2001), 125-131.
• [13] —, A fixed point conjecture for Borsuk continuous set-valued mappings, Fund. Math. 175 (2002), 69-78.
• [14] R. J. Milgram, The mod-2 spherical characteristic classes, Ann. of Math. 92 (1970), 238-261.
• [15] J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton Univ. Press, 1974.
• [16] H. Schirmer, A fixed point index for bimaps, Fund. Math. 134 (1990), 91-102.
• [17] R. Thom, Espaces fibres en sphères et carrés de Steenrod, Ann. Sci. École Norm. Sup. 69 (1952), 109-181.