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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 4, Pages 737-746

Some counterexamples and properties on generalizations of Lindelöf spaces

1Dipartimento di Matematica, Universita' di Catania, Viale A Doria, 6, Catania 95100, Italy
2Dipartimento di Matematica, Universita' di Messina, Salita Sperone, n 31, Sant' Agata, Messina 98166, Italy

Received 19 June 1992; Revised 27 September 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we give some significative counterexamples to prove that some well known generalizations of Lindelöf property are proper. Also we give some new results, we introduce and study the almost regular-Lindelof spaces as a generalization of the almost-Lindelöf spaces and as a new and significative application of the quasi-regular open subsets of [1].