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

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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.

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