The Sheaf of the Groups Formed by Topological Generalized Group over Topological Spaces

Abstract

In the present paper, we show how to construct an algebraic sheaf by means of the toplogical generalized group defined by Molaei in [1] by considering both homotopy and sheaf theory.

Keywords

• Generalized group,Topological generalized group,Whitney sum,Sheaf

References

1. Ahmadi, S. A., ” Generalized topological groups and genetic recombination.”, J Dyn Syst Geom Theor 11: 51-58, (2013).
2. Adénìran, J. O., Akinmoyewa, J. T., Şòlàìrìn, A. R. T. and Jaiyéo, T. G., “On some algebraic properties of generalized groups”, Octogon Mathematical Magazine 17: 125-134, (2009).
3. Baues, H. J., Commutator Calculus and Groups of Homotopy Classes, Cambridge, (1981).
4. Brown, R., “A geometric account of general topology., Homotopy Types and Fundemental Groupoid”, Ellis Horwood, Chichester, (1988).
5. Cartan, H., Seminaire de L’ Ecole Normale Superiure, (1950-1951).
6. Gray, B., Homotopy Theory, Academic Press New York San Francisco London, (1975).
7. Grauert, H., Remmert, R., Coherent Analytic Sheaves, Springer-Verlag, New York San Francisco London, (1984).
8. Hofmann, K. H., Mostert, P.S., Elements of Compact Semigroups, Charles E. Merrill Books, Inc., (1966).

9. Icen, I. “ Demetler uzerine”, M. SC. Thesis, Inonu University Institute of Science, Malatya, (1989).
10. Leray, J., C.R. Acad. Sci. (Paris), 232 p. 1366., (1946).
11. Mehrabi, M., Molaei, M. R. and Olomi., A. “Generalized subgroups and homomorphisms.”, Arab J Math Sci 6: 1-7, (2000). Molaei, M. R., “Connected topological generalized groups”, General Mathematics Vol. 12, No. 1: 13–22, (2004).
12. Molaei, M. R., “Topological generalized groups”, International Journal of Pure and Applied Mathematics, Vol. 2(9): 1055-1060, (2000).
13. Molaei, M. R., “Generalized groups”, International Conference on Algebra, October 14-17, Romania, (1998), Buletinul Institului Polithnic DinIasi, Tomul XLV (XLIX) :21-24, (1999).
14. Molaei, M. R., Generalized Structures Based on Completely Simple Semigroups, USA; Hadronic Press, Florida, (2005).
15. Molaei, M. R., “Generalized actions”, In: Ivailo, M. Mladenov, Gregory L. Naber, editors. Intenational Conference on Geometry, Integrability and Quantization, 1-10 September (1999); Varna, Bulgaria. Sofia: Coral Press, 175-179, (1999).
16. Spainer, E. H., Algebraic Topology, Mc Graw-Hill Publishing Company Theory, (1966).
17. Sze-Tse, H., “Structure of the homotopy groups of mapping spaces”, American Journal of Mathematics, Vol. LXXI, No:3: 574-586, (1949).
18. Whitehead, G. W., Elements of Homotopy Theory, Springer-Verlag, (1978).
19. Yıldız, C., “Topolojik uzaylar uzerinde topolojik grubun olusturdugu gruplarin demeti”, Erc. Uni. Fen Bil. Derg., 7(1): 1112-1120, (1991).