*Definition [#e9d36c4b]
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:
++V consists of open subsets of X;
++V covers X;
++V refines U;
++V is [[locally finite]] at Y.

*Remark [#ade59a2f]
-See [[1-paracompact]].

*Reference [#u6cc3a79]
K.P.Hart, J. Nagata and J.E. Vaughan, ''Encyclopedia of general topology'', Elsevier Science.