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On hereditarily Lindelöf spaces

Published online by Cambridge University Press:  17 April 2009

I. L. Reilly  and
M. K. Vamanamurthy
I. L. Reilly
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand.
M. K. Vamanamurthy
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand.
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This paper considers the question of when a space with the property that each discrete subspace is countable is hereditarily Lindelbölf. The question is answered affirmatively for the class of ROP spaces and for the class of hereditarily meta-Lindelöf spaces. A characterization of hereditarily Lindelöf spaces in terms of countable subspaces is given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 3 , June 1980 , pp. 357 - 362
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Aull, C.E., “A generalization of a theorem of Aquaro”, Bull. Austral.Math. Soc. 9 (1973), 105–108.CrossRefGoogle Scholar
[2]Bankston, Paul, “The total negation of a topological property”,Illinois J. Math..(to appear).Google Scholar
[3]Boyte, J.M., “A note on compactness and metacompactness”, Proc. Japan Acad. 46 (1970), 1084–1085.CrossRefGoogle Scholar
[4]Harley, Peter W. III and Stephenson, R.M. Jr., “Symmetrizable and related spaces”, Trans. Amer. Math. Soc. 219 (1976), 89–111.CrossRefGoogle Scholar
[5]Misra, Arvind K., “A topological view of P-spaces”, General Topology Appl. 2 (1972), 349–362.CrossRefGoogle Scholar
[6] С. Недев [Nedev, S.], “Симметри зуемые пространства и φинальнаякомпактност ть” [Symmetrizable spaces and final compactness], Dokl. Akad. Nauk SSSR 175 (1967), 532–534: Soviet Math. Dokl. 8 (1967), 890–892.Google Scholar
[7]Reilly, I.L. and Varmanamurthy, M.K., “Some topological antiproperties”, Illinois J. Math. (to appear).Google Scholar
[8]Rudin, Mary Ellen, “A normal hereditarily separable non-Lindelöf space”, Illinois J. Math. 16 (1972), 621–626.CrossRefGoogle Scholar
[9]Steen, Lynn A., Seebach, J. Arthur Jr., Counterexamples in topology (Holt, Rinehart and Winston, New York, Montreal, London, 1970).Google Scholar
[10]Stephenson, R.M. Jr., “Discrete subsets of perfectly normal spaces”, Proc. Amer. Math. Soc. 34 (1972), 605–608.CrossRefGoogle Scholar