*Definition [#w51405d9]
Let X be a topological space, Y a subspace.
Y is said to be 1-subparacompact if for every open cover U of X, there exists a [[σ-discrete]] family P of closed subsets in X such that P covers Y and that P is a partial refinement of U.

*Remark [#l7fa8fb9]
-This is not a property for a topological space, but a subspace.

*Reference [#ve629d09]
S. Kawaguchi, R. Sokei, ''Some relative properties on normality and paracompactness, and their absolute embeddings'', Comment. Math. Univ. Carolin. 46,3(2005)475-495.