*Definition [#if562447]
A subspace Y of a space X is 2-countably paracompact in X if for every countable open cover U of X, there exists a collection V of open subsets of X with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$Y%5csubset%5ccup%20V$%7d%25.png); such that V is a [[partial refinement]] of U and V is [[locally finite]] at each point of Y.

*Remark [#td546fd2]
-It is not a property for topological spaces but subspaces.

*Reference [#d34ff84f]
-Y. Yasui, ''Results on relatively countably paracompact spaces'', Questions Answers Gen. Topology, 17 (1999), 165-174.
-Y. Yasui, ''Characterizations of relatively countably paracompact spaces'', Memoirs of Osaka Kyoiku University, Ser III, 50 (2001), 1-13.
-S. Kawaguchi, ''Results on relative expandability and relative pseudocompactness'', Kyoto Univ. RIMS Kokyuroku, Vol.1492 (2006) pp.104-119