2-subparacompact

Definition

Let X be a topological space and let Y be its subspace.
Y is said to be 2-subparacompact if for every open cover U of X, there exists a family P of closed subsets in X such that P covers Y, P is a partial refinement of U and P is σ-discrete at Y.

Remark

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

Reference

Ying Ge, Subparacompact inverse images of 2-subparacompact spaces, Publications de l'Institute Mathematique, 73(87) (2003)115-120.