In this paper strongly∗o-metrizable spaces are introduced and it is shown that a space is strongly∗o-metrizable if and only if it is semistratifiable and o-metrizable (or symmetrizable);
g-metrizable spaces are strongly∗o-metrizable and hence quotient π-images of metric
spaces. As what F. Siwiec did for (second countable, metrizable and first countable)
spaces, we introduce g-developable spaces, and it is proved that a Hausdorff space is
g-developable if and only if it is symmetrizable by a symmetric under which all
convergent sequences are Cauchy.
