New Generalization of Manifolds and Orbifolds Using of Generalized Groups

Document Type : Research Paper


1 Faculty of Mathematical Sciences and Statistics, Malayer University Malayer, Iran

2 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran


Our ultimate goal in this paper is to introduce a special type of topological spaces including manifolds and also, orbifolds. Because of using of generalized groups, we call them $GG$-spaces. We will study their properties, and then we will introduce a special $GG$-space that is not manifold and orbifold. Finally we obtain conditions that cause a $GG$-space to become manifold.


[1] S.A. Ahmadi, Generalized Topological Groups and Genetic Recombination, Journal of Dynamical Systems and Geometric Theories 11, (1) (2013) 51-58.
[2] J. Araujo and J. Konieczny, Molaei's Generalized Groups are Completely Simple Semigroups, Buletinul Institului Polithnic Din Iasi 48, (52) (2004) 1-5.
[3] J.E. Borzellino and V. Brunsden, Determination of the Topological Structure of an Orbifold by its Group of Orbifold Di eomorphisms, Journal of Lie Theory 13 (2003) 311-327.
[4] N. Ebrahimi, Left Invariant Vector Fields of a Class of Top Spaces, Balkan J. Geom. Appl. 14 (2012) 37-44.
[5] M.R. Farhangdoost, Action of Generalized Groups on Manifolds, Acta Math. Univ.Comenianae. LXXX, (2) (2011) 229-235.
[6] I.M. Lee, Introduction to Smooth Manifolds, Springer- Verlag New York (2003).
[7] H. Maleki and M.R. Molaei, T-Spaces, Turk J Math 39, (6) (2015) 851-863.
[8] M.R. Molaei, Generalized Actions, Proceedings of the First International Conference on Geometry, Integrability and Quantization, Coral Press Scienti c Publishing September (1999) 175-180.
[9] M.R. Molaei, Generalized Groups, Buletinul Institului Polithnic Din Iasi XLV(XLIX (1999) 21-24.
[10] M.R. Molaei, Topological Generalized Groups, International Journal of Applied Mathematics 2, (9) (2000) 1055-1060.
[11] M.R. Molaei, Top Spaces, J. Interdiscip. Math. 7, (2) (2004) 173-181.
[12] M.R. Molaei, Mathematical Structures Based on Completely Simple Semigroups,Hadronic press 2005.
[13] M.R. Molaei, Complete Semi-dynamical Systems, Journal of Dynamical Systems and Geometric Theories 3, (2) (2005) 95-107.
[14] M.R. Molaei and G.S. Khadekar and M.R. Farhangdoost, On Top Spaces, Balkan J. Geom. Appl. 11, (1) (2009) 101-106.
[15] I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. USA 42 (1956) 359-363.
[16] W. Thurston, The Geometry and Topology of Three-Manifolds, New Jersey: Princeton University Press (1997).
[17] L.W. Tu, An Introduction to Manifolds, Springer (2010).
  • Receive Date: 06 May 2021
  • Revise Date: 24 December 2021
  • Accept Date: 28 January 2022
  • First Publish Date: 04 February 2022