Geodesic
The Almost Lindelöf Degree
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 452-455

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In [A], Arhangel'skii showed that for any T2 space X, |X|≤2L(x)χ(x), where L(X) is the Lindelöf degree of X and χ(X) is the character of X.In [B], Bell, Ginsburg and Woods improved this result, assuming normality, by showing that for T4 spaces X, |X|≤2wL(x)χ(x), where wL(X) is the weak Lindelöf degree of X.We introduce below a new cardinal function aL(X), the almost Lindelöf degree of X, which agrees with L(X) on T3 spaces, but which is often smaller than L(X) on T2 spaces, and show that for T2 spaces X,
DOI : 10.4153/CMB-1984-070-2
Mots-clés : 54A25, 54D20 
Willard, S.; Dissanayake, U. N. B. The Almost Lindelöf Degree. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 452-455. doi: 10.4153/CMB-1984-070-2
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[A] [A] Arhangel'skii, A. V., On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dok. 10 (1969), 951-955. Google Scholar

[B] [B] Bell, M. J., Ginsburg, J. N. and Woods, G., Cardinal inequalities for topological spaces involving the weak Lindelü number, Pacific J. Math. 79 (1978), 37-45. Google Scholar | DOI

[J] [J] Juhasz, I., Cardinal functions in Topology - ten years later, Math. Centre Tract #123, Math, centrum, Amsterdam, 1980. Google Scholar

[W] [W] Willard, S., General Topology, Addison-Wesley, Reading, Mass., 1968. Google Scholar

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