Convergence semigroup actions: generalized quotients

H. Boustique

United States

University of Central Florida

Piotr Mikusinski

United States

University of Central Florida

Gary Richardson

United States

University of Central Florida

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

Submitted: 2013-09-30

|

Accepted: 2013-09-30

|
DOI: https://doi.org/10.4995/agt.2009.1731
Funding Data

Downloads

Keywords:

Continuous action, Convergence space, Quotient map, Semigroup

Supporting agencies:

This research was not funded

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
Show more Show less

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.

Show more Show less