A note on star Lindelöf, first countable and normal spaces
Wei-Feng Xuan (2017)
Mathematica Bohemica
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A topological space is said to be star Lindelöf if for any open cover of there is a Lindelöf subspace such that . The “extent” of is the supremum of the cardinalities of closed discrete subsets of . We prove that under every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under , which shows that a star Lindelöf, first countable and normal space may not have countable extent.