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Keywords:
Lefschetz number; fixed point; topological vector spaces; Klee admissible spaces; absolute neighborhood multi-retracts; approximative absolute neighborhood multi-retracts; multicore
Lefschetz number; fixed point; topological vector spaces; Klee admissible spaces; absolute neighborhood multi-retracts; approximative absolute neighborhood multi-retracts; multicore
Summary:
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
References:
[1] Agarwal, G. P., O’Regan, D.: A note on the Lefschetz fixed point theorem for admissible spaces. Bull. Korean Math. Soc. 42, 2 (2005), 307–313. DOI 10.4134/BKMS.2005.42.2.307 | MR 2153878 | Zbl 1089.47040
[2] Andres, J., Górniewicz, L.: Topological principles for boundary value problems. Kluwer, Dordrecht, 2003.
[3] Bogatyi, S. A.: Approximative and fundamental retracts. Math. USSR Sb. 22 (1974), 91–103. DOI 10.1070/SM1974v022n01ABEH001687 | MR 0336695
[4] Borsuk, K.: Theory of Shape. Lect. Notes Ser. 28, Matematisk Institut, Aarhus Universitet, Aarhus, 1971. MR 0293602 | Zbl 0232.55021
[5] Clapp, M. H.: On a generalization of absolute neighborhood retracts. Fund. Math. 70 (1971), 117–130. MR 0286081 | Zbl 0231.54012
[6] Eilenberg, S., Steenrod, N.: Foundations of Algebraic Topology. New Jersey Princeton University Press, Princeton, 1952. MR 0050886 | Zbl 0047.41402
[7] Fournier, G., Granas, A.: The Lefschetz fixed point theorem for some classes of non-metrizable spaces. J. Math. Pures et Appl. 52 (1973), 271–284. MR 0339116 | Zbl 0294.54034
[8] Górniewicz, L.: Topological methods in fixed point theory of multi-valued mappings. Springer, New York–Berlin–Heidelberg, 2006.
[9] Górniewicz, L., Rozpłoch-Nowakowska, D.: The Lefschetz fixed point theory for morphisms in topological vector spaces. Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center 20 (2002), 315–333. MR 1962224 | Zbl 1031.55002
[10] Górniewicz, L., Ślosarski, M.: Once more on the Lefschetz fixed point theorem. Bull. Polish Acad. Sci. Math. 55 (2007), 161–170. DOI 10.4064/ba55-2-7 | MR 2318637 | Zbl 1122.55002
[11] Górniewicz, L., Ślosarski, M.: Fixed points of mappings in Klee admissible spaces. Control and Cybernetics 36, 3 (2007). MR 2376056
[12] Granas, A.: Generalizing the Hopf–Lefschetz fixed point theorem for non-compact ANR’s. In: Symp. Inf. Dim. Topol., Baton-Rouge, 1967.
[13] Granas, A., Dugundji, J.: Fixed Point Theory. Springer, Berlin–Heidelberg–New York, 2003. MR 1987179 | Zbl 1025.47002
[14] Jaworowski, J.: Continuous Homology Properties of Approximative Retracts. Bulletin de L’Academie Polonaise des Sciences 18, 7 (1970). MR 0267574 | Zbl 0199.26004
[15] Krathausen, C., Müller, G., Reinermann, J., Schöneberg, R.: New Fixed Point Theorems for Compact and Nonexpansive Mappings and Applications to Hammerstein Equations. Sonderforschungsbereich 72, Approximation und Optimierung, Universität Bonn, preprint no. 92, 1976.
[16] Kryszewski, W.: The Lefschetz type theorem for a class of noncompact mappings. Suppl. Rend. Circ. Mat. Palermo 14, 2 (1987), 365–384. MR 0920869 | Zbl 0641.55002
[17] Leray, J., Schauder, J.: Topologie et $\acute{e}$quations fonctionnelles. Ann. Sci. Ecole Norm. Sup. 51 (1934).
[18] Peitgen, H. O.: On the Lefschetz number for iterates of continuous mappings. Proc. AMS 54 (1976), 441–444. MR 0391074 | Zbl 0316.55006
[19] Skiba, R., Ślosarski, M.: On a generalization of absolute neighborhood retracts. Topology and its Applications 156 (2009), 697–709. MR 2492955 | Zbl 1166.54008
[20] Ślosarski, M.: On a generalization of approximative absolute neighborhood retracts. Fixed Point Theory 10, 2 (2009). MR 2569006 | Zbl 1185.55002
[21] Ślosarski, M.: Fixed points of multivalued mappings in Hausdorff topological spaces. Nonlinear Analysis Forum 13, 1 (2008), 39–48. MR 2808029
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