Convergence semigroup actions: generalized quotients


  • H. Boustique University of Central Florida
  • Piotr Mikusinski University of Central Florida
  • Gary Richardson University of Central Florida



Continuous action, Convergence space, Quotient map, Semigroup


Continuous actions of a convergence semigroup are investigated in the category of convergence spaces. Invariance properties of actions as well as properties of a generalized quotient space are presented


Download data is not yet available.

Author Biography

Gary Richardson, University of Central Florida

Department of Mathematics, University of Central Florida,Orlando, FL 32816, USA, fax: (407) 823-6253, tel: (407) 823-2753


J. Burzyk, C. Ferens and P. Mikusinski, On the topology of generalized quotients, Applied Gen. Top. 9 (2008), 205–212.

D. Kent, Convergence quotient maps, Fund. Math. 65 (1969), 197–205.

D. Kent and G. Richardson, Open and proper maps between convergence spaces, Czech. Math. J. 23(1973), 15–23.

D. Kent and G. Richardson, The regularity series of a convergence space, Bull. Austral. Math. Soc. 13 (1975), 21–44.

M. Khosravi, Pseudoquotients: Construction, applications, and their Fourier transform, Ph.D. dissertation, Univ. of Central Florida, Orlando, FL, 2008.

P. Mikusinski, Boehmians and generalized functions, Acta Math. Hung. 51 (1988), 271–281.

P. Mikusinski, Generalized quotients with applications in analysis, Methods and Applications of Anal. 10 (2003), 377–386.

W. Park, Convergence structures on homeomorphism groups, Math. Ann. 199 (1972), 45–54.

W. Park, A note on the homeomorphism group of the rational numbers, Proc. Amer. Math. Soc. 42 (1974), 625–626.

N. Rath, Action of convergence groups, Topology Proceedings 27 (2003), 601–612.


How to Cite

H. Boustique, P. Mikusinski, and G. Richardson, “Convergence semigroup actions: generalized quotients”, Appl. Gen. Topol., vol. 10, no. 2, pp. 173–186, Oct. 2009.



Regular Articles