Cardinalities of some Lindelöf and \(\omega_1\)-Lindelöf \(T_1/T_2\)-spaces
Bounds on the cardinality of a space and on its Lindelöf number are considered. The main results are that if \(X\) has countable tightness and countable pseudocharacter then \(| X| \leq{\mathfrak c}\) if either \(X\) is Lindelöf, paracompact and T\(_1\) or \(X\) is \(\omega_1\)-Lindelöf and realcompact, and \(| X| \leq2^{\mathfrak c}\) if \(X\) is first countable, T\(_2\) and \(\omega_1\)-Lindelöf. A number of relevant questions are asked.
scientific article; zbMATH DE number 2104481