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Generalized products of weakly m — n compact spaces, I

Part of: Fairly general properties

Published online by Cambridge University Press:  09 April 2009

U. N. B. Dissanayake
U. N. B. Dissanayake
Affiliation:
Department of Mathematics University of AlbertaEdmonton, AlbertaCanadaT6G 2G1
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Abstract

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A topological space X is said to be weakly-Lindelöf if and only if every open cover of X has a countable sub-family with dense union. We know that products of two Lindelöf spaces need not be weakly-Lindelöf. In this paper we obtain non-trivial sufficient conditions on small sub-products to ensure the producitivity of the property weakly-Lindelöf with respect to arbitrary products.

Keywords

weakly-Lindelöf spacesTk-spacesk = 2weakly m — n compact spacesweakly ∞ — n compact spacesk-box topologyγ-weak topological sumsregular cardinalssingular cardinalsstrongly γ-inaccessible cardinalsdensity number.

MSC classification

Secondary: 54D30: Compactness
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 143 - 151
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Alexandroff, P. and Hopf, H., Topologie I (Springer-Verlag, Berlin, 1935).CrossRefGoogle Scholar
[2]Comfort, W. W. and Negrepontis, S., The theory of ultrafilters (Springer-Verlag, Berlin and New York, 1974).CrossRefGoogle Scholar
[3]Comfort, W. W., ‘Compactness-like properties for generalized weak-topological sums’, Pacific J. Math. 60 (1975), 31–37.CrossRefGoogle Scholar
[4]Enderton, H. B., Elements of set theory (Academic Press, New York and London, 1977).Google Scholar
[5]Gal, I. S., ‘On the theory of (m, n) compact topological spaces’, Pacific J. Math. 58 (1958), 721–734.CrossRefGoogle Scholar
[6]Gillman, L. and Jerison, M., Rings of continuous functions (D. Van Nostrand, Princeton, New Jersey, 1960).CrossRefGoogle Scholar
[7]Hajek, D. W. and Todd, A. R., ‘Lightly compact spaces and infra H-closed spaces’, Proc. Amer. Math. Soc. 48 (1975), 479–482.Google Scholar
[8]Hajnal, A. and Juhasz, I., ‘On the product of weakly-Lindelöf spaces’, Proc. Amer. Math. Soc. 48 (1975), 454–456.Google Scholar
[9]Jech, I., Set theory (Academic Press, London, 1978).Google Scholar
[10]Ulmer, M., ‘Products of weakly-ℵ-compact spaces’, Trans. Amer. Math. Soc. 170 (1972), 279–284.Google Scholar