*Definition [#c7044a72]
A topological space is called subparacompact if every open cover of X has a [[σ-discrete]] closed refinement.
*Property [#y8409ed8]
-Every metacompact space in which every closed subset is Gδ is subparacompact.

*Remark [#yfaf8d91]
-It is also called [[σ-paracompact]].

*Reference [#v8830092]
-Dennis K. Burke, ''On subcompact spaces'', Proc. Amer. Math. Soc. Vol.23 No.3 (1969) pp.655-663.
-R. E. Hodel, ''A note on subparacompact spaces'',  Proceedings of the American Mathematical Society, 1970.