strictly Aull-paracompact

Definition

• A subspace Y is said to be Aull-paracompact in X if for every σ-discrete collection U of open subsets of X with Y ⊂ ∪U, there exists a collection V of open subsets of X with Y = ∪V such that V is a partial refinement? of U and V is locally finite at each point of Y .

Reference

• Arhangelʹskii, A. V.(1-OH), and Gordienko, I. Ju.(RS-MOSC), Relative symmetrizability and metrizability. (English summary) , Comment. Math. Univ. Carolin. 37 (1996), no. 4, 757--774.