*Definition [#c2dcd276]
A subset Y of a space X is said to be 2-paracompact in X iff for every 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 [#q940b1d0]
-This is not a property for topological spaces, but subspaces.
-The term "2-paracompact" is often shortened to "paracompact".
-See [[1-paracompact]], [[3-paracompact]].

*Reference [#b729aae6]
K.P.Hart, J. Nagata and J.E. Vaughan, ''Encyclopedia of general topology'', Elsevier Science