*Definition [#r2781c78]
-A subspace Y of a space X is said to be 1-metacompact in X if for every open cover U of X, there exists an open refinement V of U such that V is [[point-finite]] at every y ∈ Y.

*Reference [#wba3ff7e]
-Kawaguchi, Shinji(J-TSUKS-GAS) and Sokei, Ryoken(J-TOKYG-HS) , ''Some relative properties on normality and paracompactness, and their absolute embeddings. (English summary)'', 
Comment. Math. Univ. Carolin. 46 (2005), no. 3, 475--495.