Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-27T10:50:11.421Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Stone-Čeck compactification of an orbit space

Published online by Cambridge University Press:  17 April 2009

Kavita Srivastava
Kavita Srivastava
Affiliation:
Senior Research Fellow, Allahabad Mathematical Society, Vijay Niwas, 198, Mumfordganj, ALLARABAD 211002, India.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By extending the given action of a discrete group G on a Tychonoff space X to βX, it is proved that the Stone-Čech compactification of the orbit space of X is the orbit space of the Stone-Čech compactification βX of X, when G is finite. The notion of G-retractive spaces is introduced and it is proved that the orbit space of a G-retractive space with G finite, is G-retractive.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 435 - 439
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bredon, G.E., Introduction to compact transformation groups., (Academic Press, New York and London; 1972).Google Scholar
[2]Comfort, W.W., Retractions and other continuous maps from βX onto βX - X”, Trans. Amer. Math. Soc. 114 (1965), 1–9.Google Scholar
[3]Gillman, L. and Jerison, M., Rings of continuous functions, (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1969).Google Scholar
[4]Walker, R.C., The Stone-Čech compactification, (Springer-Verlag, Berlin; Heidelberg; New York; 1974).CrossRefGoogle Scholar