Convergence semigroup actions: generalized quotients

Authors

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

DOI:

https://doi.org/10.4995/agt.2009.1731

Keywords:

Continuous action, Convergence space, Quotient map, Semigroup

Abstract

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

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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

References

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. http://dx.doi.org/10.1017/S0004972700024229

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. http://dx.doi.org/10.1007/BF01903334

P. Mikusinski, Generalized quotients with applications in analysis, Methods and Applications of Anal. 10 (2003), 377–386. http://dx.doi.org/10.4310/MAA.2003.v10.n3.a4

W. Park, Convergence structures on homeomorphism groups, Math. Ann. 199 (1972), 45–54. http://dx.doi.org/10.1007/BF01419575

W. Park, A note on the homeomorphism group of the rational numbers, Proc. Amer. Math. Soc. 42 (1974), 625–626. http://dx.doi.org/10.1090/S0002-9939-1974-0341368-9

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

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How to Cite

[1]
H. Boustique, P. Mikusinski, and G. Richardson, “Convergence semigroup actions: generalized quotients”, Appl. Gen. Topol., vol. 10, no. 2, pp. 173–186, Oct. 2009.

Issue

Section

Regular Articles