I try to study the Lindelöf number of topological space. Are there some classical books or papers or useful links on this? Thanks!
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The classic reference for cardinal functions in topology is István Juhász, Cardinal functions in topology, Math. Centre Tracts 34, Amsterdam, 1971. It was superseded by his Cardinal functions in topology: ten years later, Math Centre Tracts 123, Amsterdam, 1980, with a second printing in 1983. Both are freely available in PDF here: search on cardinal functions in the Title field. (There are also direct links to the PDFs here.) The articles Cardinal Functions I and Cardinal Functions II by Richard Hodel and István Juhász, respectively, in the Handbook of Set-Theoretic Topology, Kenneth Kunen and Jerry E. Vaughan, eds., North-Holland, 1988, are also worth a look. All of these have copious references.
Of course all of those references are at least $25$ years old; a search on Lindelöf degree and Lindelöf number will turn up a great deal of more recent material on this and related topics. But they should still be a useful starting point.