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On some properties of linearly Lindelöf spaces. (English) Zbl 0964.54018
Summary: Improving an earlier result in [the authors, Proc. Am. Math. Soc. 127, No. 8, 2449-2458 (1999; Zbl 0930.54003)], we show that the cardinality of a sequential linearly Lindelöf Tikhonov space $$X$$ does not exceed $$2^\omega$$ if and only if the pseudocharacter of $$X$$ does not exceed $$2^\omega$$. We also establish that every locally metrizable linearly Lindelöf regular space is separable and metrizable.

##### MSC:
 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54E35 Metric spaces, metrizability
Zbl 0930.54003
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