order totally paracompact

Definition

A space X is said to be order totally paracompact if for every open base B of X, there exists a order locally finite open covering U of X such that for each V in U, there exists A in B such that A contains V and boundary A contains boundary V.

Reference

Y Hayashi, A regular space which is not countably metacompact, Memoirs of the konan
Univ. (1967), 31-43.
M. K. Singal, Some Generalizations of Paracompactness, Proceedings of the Kanpur topological conference, 1968. Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971. pp. 245-263.