In this paper, spaces with $\sigma $-locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or $g$-first countable spaces with $\sigma $-locally countable $cs$-networks).
@article{107989, author = {Zhaowen Li}, title = {Spaces with $\sigma$-locally countable weak-bases}, journal = {Archivum Mathematicum}, volume = {042}, year = {2006}, pages = {135-140}, zbl = {1164.54369}, mrnumber = {2240190}, language = {en}, url = {http://dml.mathdoc.fr/item/107989} }
Li, Zhaowen. Spaces with $\sigma$-locally countable weak-bases. Archivum Mathematicum, Tome 042 (2006) pp. 135-140. http://gdmltest.u-ga.fr/item/107989/
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