Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-01T13:40:03.043Z Has data issue: false hasContentIssue false

Maximal topologies

Published online by Cambridge University Press:  09 April 2009

Asit Baran Raha
Affiliation:
Indian Statistical Institute203 Barrackpore Trunk RdCalcutta – 35India
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.

This article is devoted to studying maximal π spaces where π = Lindelöf, countably compact, connected, lightly compact or pseudocompact. Necessary and sufficient conditions for Lindelöf or countably compact spaces to be maximal Lindelöf or maximal countably compact have been obtained. On the other hand only necessary conditions for maximal π spaces have been deduced where π = connected, lightly compact or pseudocompact.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bourbaki, NGeneral Topology {Part 1) (Addison-Wesley Publishing Company, Reading, Massachussetts, 1966)Google Scholar
[2]Dieudonné, JNotes de Teratopologie (I)’, Revue scientifique, 1939, p.39.Google Scholar
[3]Gillman, Leonard and Jerisen, M., Rings of continuous functions, (D. Van Nostrand and Co., Princeton, New Jersey, (1960).CrossRefGoogle Scholar
[4]Mioduszewski, J. and Rudolf, L., ‘H-closed and extremally disconnected Hausdorff spaces’, Dissertations Mathematicase LXVI (1969).Google Scholar
[5]Scarborough, C. T. and Stephenson, R. M. Jr, ‘ Minimal topologies’, Colloqium. Math. 19 (1968), 215219.CrossRefGoogle Scholar
[6]Smythe, N. and Wilkins, C. A., ‘Minimal Hausdorff and maximal compact spaces’, J. Austral. Math. Soc.. 3 (1963), 167171.CrossRefGoogle Scholar
[7]Stephenson, R. M. Jr., ‘Pseudocompact spaces’, Trans. Amer. Math. Soc. 134 (1968), 437448.CrossRefGoogle Scholar
[8]Thomas, J. P.Maximal connected topologies’, Jour. Austral. Math. Soc. 8 (1968). 700705.CrossRefGoogle Scholar
[9]Vaidynathaswamy, R. Treatise on set topology (Ind. Math. Soc. Madras (1947).Google Scholar