almost countably paracompact

Definition

A topological space X is called almost countably paracompact if for every countable open cover U of X, there exists a family of open subsets such that every member of V is contained in some member of U and that the closure of V covers X.

Remark

• Note that V is not necessarily a refinement of U, which is not required to cover X.
• See almost paracompact.

Reference

M. K. Singal and Shashi Prabha Arya, On M-Paracompact Spaces, Math. Ann. 181, 119--133 (1969).