σ-totally paracompact

Definition

A space X is said to be σ-totally paracompact if for every open base B of X, there exists a σ-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

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.