1-paracompact

Definition

A subset Y of a space X is said to be 1-paracompact in X iff for every open cover U of X, there exists a collection V which satisfies:

1. V consists of open subsets of X;
2. V covers X;
3. V refines U;
4. V is locally finite at Y.

Remark

• This is not a property for topological spaces, but subspaces.
• See 2-paracompact, 3-paracompact.

Reference

K.P.Hart, J. Nagata and J.E. Vaughan, Encyclopedia of general topology, Elsevier Science