Abstract:In [{\it The sup = max problem for the extent of generalized metric spaces\/}, Comment. Math. Univ. Carolin. (The special issue devoted to \v Cech) {\bf 54} (2013), no.~2, 245--257], the author and Yajima discussed the sup = max problem for the extent and the Lindel\"of degree of generalized metric spaces: (strict) $p$-spaces, (strong) $\Sigma $-spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindel\"of degree of spaces having $G_\delta $-diagonals and for the extent of spaces having point-countable bases is considered.
Keywords: extent; Lindel\"of degree; $G_\delta $-diagonal; point-countable base
DOI: DOI 10.147.12/1213-7243.015.108
AMS Subject Classification: 54A25 54D20 03E10