## The almost Lindelöf degree.(English)Zbl 0551.54003

In Dokl. Akad. Nauk SSSR 187, 967-970 (1969; Zbl 0191.209) A. V. Arkhangel’skij showed that for any $$T_ 2$$ space X, $$| X| \leq 2^{L(X)\chi(X)},$$ where $$L(X)$$ is the Lindelöf degree of $$X$$ and $$\chi(X)$$ is the character of X. In Pac. J. Math. 79, 37-45 (1978; 367.54003) M. Bell, J. Ginsburg and G. Woods improved this result, assuming normality, by showing that for $$T_ 4$$ spaces X,$$| X| \leq 2^{wL(X)\chi(X)},$$ where wL(X) is the weak Lindelöf degree of $$X$$. We introduce a new cardinal function aL(X), the almost Lindelöf degree of $$X$$, which agrees with $$L(X)$$ on $$T_ 3$$ spaces, but which is often smaller than L(X) on $$T_ 2$$ spaces, and show that for $$T_ 2$$ spaces X, $$[X]\leq 2^{aL(X)\chi(X)}.$$

### MSC:

 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)

Zbl 0191.209
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