countably 1-paracompact

Definition

A subset Y of a topological space X is said to be countably 1-paracompact if for every countable 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

• See 1-paracompact.

Reference

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