1-metacompact

Definition

• 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

• 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.