countably 3-paracompact

Definition

A subset Y of a space X is said to be countably 3-paracompact in X iff for every countable open cover U of X, there exists a collection V which satisfies:

1. V consists of open subsets of Y;
2. V covers Y;
3. V is a partial refinement? of U;
4. V is locally finite at Y.

Remark

• See 3-paracompact.

Reference

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