Abstract
In [The sup = max problem for the extent of generalized metric spaces, Comment. Math. Univ. Carolin. The special issue devoted to Cech 54 (2013), no. 2, 245–257], the author and Yajima discussed the sup = max problem for the extent and the Lindelof degree of generalized metric spaces: (strict) $p$-spaces, (strong) $\Sigma $-spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelof degree of spaces having $G_\delta $-diagonals and for the extent of spaces having point-countable bases is considered.
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