1-subparacompact

Definition

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

• This is not a property for a topological space, but a subspace.

Reference

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