Convergence S-compactifications

Authors

  • Bernd Losert University of Central Florida
  • Gary Richardson University of Central Florida

DOI:

https://doi.org/10.4995/agt.2014.3156

Keywords:

convergence space, convergence semigroup, continuous action, S-compactification.

Abstract

Properties of continuous actions on convergence spaces are investigated. The primary focus is the characterization as to when a continuous action on a convergence space can be continuously extended to an action on a compactification of the convergence space. The largest and smallest such compactifications are studied.

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References

H. Boustique, P. Mikusinski and G. Richardson, Convergence semigroup actions: generalized quotients, Appl. Gen. Topol. 10 (2009), 173 -186.

(http://dx.doi.org/10.4995/agt.2009.1731)

H. Boustique, P. Mikusinski and G. Richardson, Convergence semigroup categories, Appl. Gen. Topol. 11, no. 2 (2010), 67-88.

(http://dx.doi.org/10.4995/agt.2010.1709)

J. de Vries, On the existence of G -compactifications, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 26, no. 3 (1978), 275-280.

W. H. Gottschalk and G. A. Hedlund, Topological D ynamics, volume 36. American Mathematical Society, 1955.

H. H. Keller, Die Limes-uniformisierbarkeit der Limesräume, Mathematische Annalen 176, no. 4 (1968), 334-341.

(http://dx.doi.org/10.1007/BF02052894)

D. C. Kent and G. D. Richardson, Regular compactifications of convergence spaces, Proc. Amer. Math. Soc. 31 (1972), 571-573.

(http://dx.doi.org/10.1090/S0002-9939-1972-0286074-2)

D. C. Kent and G. D. Richardson, Open and proper maps between convergence spaces, Czechoslovak Mathematical Journal 23, no. 1 (1973), 15-23.

D. C. Kent and G. D. Richardson, Locally compact convergence spaces, The Michigan Mathematical Journal 22, no. 4 (1975), 353-360.

D. C. Kent and G. D. Richardson, Compactifications of convergence spaces, Internat. J. Math. Math. Sci. 2, no. 3 (1979), 345-368.

(http://dx.doi.org/10.1155/S0161171279000302)

E. Lowen-Colebunders, Function Classes of Cauchy Continuous Maps, M. Dekker, 1989.

G. Preuss, Foundations of Topology: An Approach to Convenient Topology, Kluwer Academic Publishers, Dordrecht, 2002.

(http://dx.doi.org/10.1007/978-94-010-0489-3)

E. E. Reed, Completions of uniform convergence spaces, Mathematische Annalen 194, no. 2 (1971), 83-108.

(http://dx.doi.org/10.1007/BF01362537)

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Published

2014-07-25

How to Cite

[1]
B. Losert and G. Richardson, “Convergence S-compactifications”, Appl. Gen. Topol., vol. 15, no. 2, pp. 121–136, Jul. 2014.

Issue

Section

Regular Articles