Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-08T19:13:46.847Z Has data issue: false hasContentIssue false

On the largest Hausdorff compactification of a Hausdorff convergence space

Published online by Cambridge University Press:  17 April 2009

Vinod-Kumar
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, India.
Rights & Permissions [Opens in a new window]

Abstract

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.

For a Hausdorff convergence space, necessary and sufficient conditions for its Richardson compactification to be the largest Hausdorff compactification are found and by modifying the convergence structure of the Richardson compactification, it is shown that the largest Hausdorff compactification, whenever it exists, is given by that modified Richardson compactification.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Kent, D.C., “Convergence quotient maps”, Fund. Math. 65 (1969), 197205.CrossRefGoogle Scholar
[2]Rao, C.J.M., “On smallest compactification for convergence spaces”, Proc. Amer. Math. Soc. 44 (1974), 225230.CrossRefGoogle Scholar
[3]Rao, C.J.M., “On largest Hausdorff compactification for convergence spaces”, Bull. Austral. Math. Soc. 12 (1975), 7379.CrossRefGoogle Scholar
[4]Mohan Rao, Challa Jagan, On extremal compactifications of convergence spaces (Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, 1975).Google Scholar
[5]Richardson, G.D., “A Stone-Čech compactification for limit spaces”, Proc. Amer. Math. Soc. 25 (1970), 403404.Google Scholar
[6]Richardson, G.D. and Kent, D.C., “Regular compactifications of convergence spaces”, Proc. Amer. Math. Soc. 31 (1972), 571573.CrossRefGoogle Scholar