On the metrizability number and related invariants of spaces, II

This is a continuation of the study of the metrizability number and the first countability number for various classes of compact Hausdorff spaces started by Ismail and Szymanski (1995). It is shown that if X is a compact LOTS, then w(X) ⩽ ω·m(X). Also, if X is the one-point compactification of an uncountable discrete space, then ω1 ⩽ m(Xω) ⩽ 2ω. Furthermore, under the singular cardinals hypothesis, for a large class of spaces of cardinality > 2ω, the first countability number, the metrizability number and the cardinality coincide.