α-almost $\mathbb{R}$-paracompact

Definition

A subset A of a space X is said to be α-almost -paracompct iff for every X-open cover U with of A there exists an X-locally finite family of X-open subsets V which refines U and is that the family of X-closures of members of V forms a cover of A.

Reference

• Cao Ji-Ling, Weakly closed multifunctions and paracompactness, Internat. J. Math and Math. Sci. Vol.16, No.2, pp.345-350 (1993)