strictly paracompact

Definition

Let A be a subset of a topological space. A is called strictly paracompact if for every X-open cover U of A, there exists an X-open X-locally finite subfamily V which refines U and covers A.

Reference

V. Popa, A note on weakly and almost continuous multifunctions, Univ. u Novom Sadu Zb. Rad. Prirod. -Mat. Fak. Ser. Mat. 21, 2 (1991), 31-38.