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The Almost Lindelöf Degree

Published online by Cambridge University Press:  20 November 2018

S. Willard  and
U. N. B. Dissanayake
S. Willard
Affiliation:
The University of Alberta, Edmonton, Alberta
U. N. B. Dissanayake
Affiliation:
The University of Alberta, Edmonton, Alberta
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Abstract

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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,

Keywords

54A2554D20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 452 - 455
Copyright
Copyright © Canadian Mathematical Society 1984

References

[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] 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.CrossRefGoogle Scholar
[J] Juhasz, I., Cardinal functions in Topology - ten years later, Math. Centre Tract #123, Math, centrum, Amsterdam, 1980.Google Scholar
[W] Willard, S., General Topology, Addison-Wesley, Reading, Mass., 1968.Google Scholar