*Definition [#td4abe8a]
A subset Y of a space X is said to be 1-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 X;
++V refines U;
++V is [[locally finite]] at Y.

*Remark [#zb56946d]
-This is not a property for topological spaces, but subspaces.
-See [[2-paracompact]], [[3-paracompact]].

*Reference [#v38dd87b]
K.P.Hart, J. Nagata and J.E. Vaughan, ''Encyclopedia of general topology'', Elsevier Science