Definition
The space X is said to be strongly countably paracompact if each countable open covering of X admits as a refinement of a star-finite open covering.
Remark
Reference
M. K. Singal, Some Generalizations of Paracompactness, Proceedings of the Kanpur topological conference, 1968. Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971. pp. 245-263.