*Definition [#c2dcd276]
A subset Y of a space X is said to be countably 2-paracompact in X iff for every countable open cover U of X, there exists a collection V which satisfies:
++V consists of open subsets of X;
++V covers Y;
++V is a [[partial refinement]] of U;
++V is [[locally finite]] at Y.

*Remark [#k1bffb6d]
-See [[2-paracompact]].

*Reference [#ma34fd0f]
K.P.Hart, J. Nagata and J.E. Vaughan, ''Encyclopedia of general topology'', Elsevier Science.