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

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

PDF

___

Molaei, M. R., “Generalized groups”, International Conference on Algebra, October 14-17, Romania, (1998), Buletinul Institului Polithnic DinIasi, Tomul XLV (XLIX) :21-24, (1999).
Adéníran, J. O., Akinmoyewa, J. T., Şòlárìn, A. R. T. and Jaiyé?lá, T. G., “ On some algebraic algebraic properties of generalized groups”, Octogon Mathematical Magazine 17: 125-134, (2009).
Mehrabi, M., Molaei, M. R. and Olomi., A. “Generalized subgroups and homomorphisms.”, Arab J Math Sci 6: 1-7, (2000).
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).
Molaei, M. R., “Topological generalized groups”, International Journal of Pure and Applied Mathematics 2(9): 1055-1060, (2000).
Molaei, M. R., “Connected topological generalized groups”, General Mathematics 12(1): 13–22, (2004).
Molaei, M. R., Generalized Structures Based on Completely Simple Semigroups, Hadronic Press, Florida, USA, (2005).
Hawking S. W. and Ellis G.F.R., The Large Scale Structure of Space-Time, Cambridge University Press, New York, (1987).
Ahmadi, S. A., “Generalized topological groups and genetic recombination”, J. Dyn. Syst. Geom Theor. 11: 51-58, (2013).
Leray, J., “L’anneau d’homologie d’une repr ́esentation”, C.R. Acad. Sci. 222, Paris, 1419-1422, (1946).
Cartan, H., Seminaire de L’ Ecole Normale Superiure, Paris, (1950-1951).
Yildiz, C., “Topolojik uzaylar uzerinde topolojik grubun olusturdugu grupların demeti”, Erc.. Uni. Fen Bil. Derg., 7(1): 1112-1120, (1991).
Farhangdoost M. R. and Nasirzade T., “Geometrical categories of generalized Lie groups and Lie group-groupoids”, Iran J Sci Technol A: 69-73, (2013).
Hofmann, K. H. and Mostert, P.S., Elements of Compact Semigroups, Charles E. Merrill Books, Inc., Colombus, Ohio, (1966).
Spainer, E. H., Algebraic Topology, Mc Graw-Hill Publishing Company Theory, Springer-Verlag New York, (1966).
Brown, R., “Topology: A geometric account of general topology., Homotopy Types and Fundemental Groupoid”, Ellis Horwood, Chichester, (1988).
Grauert, H. and Remmert, R., Coherent Analytic Sheaves, Springer-Verlag, New York San Francisco London, (1984).
Ulucay C., Fonksiyonlar Teorisi ve Riemann Yüzeyleri K.T.U Temel Bilimler Fakultesi Yayinlari, Ankara Universitesi Basımevi, Ankara, (1978).
Icen, I., “Demetler uzerine”, MSc. Thesis, Inönü University Institute of Science, Malatya, (1989).
Baues, H. J., Commutator Calculus and Groups of Homotopy Classes, London Mathematical Society, Cambridge, (1981).
Gray, B., Homotopy Theory, Academic Press, New York San Francisco London, (1975).
Sze-Tse, H., “Structure of the homotopy groups of mapping spaces”, American Journal of Mathematics LXXI (3): 574-586, (1949)..
Whitehead, G. W., Elements of Homotopy Theory, Springer-Verlag, New York , (1978).