quasi-paracompact

Definition

A topological space is said to be quasi-paracompact iff every open cover has a locally finite shrinking.

Property

The following are equivalent for a space T:

1. T is quasi-paracompact;
2. T is a T_4 space and each open cover has an open locally finite refinement.
3. For every open cover {U_i}, there exists an open locally finite cover {W_j} such that {cl(W_j)} refines {U_i}.

Reference

G. Richter and A. Vauth, Fibrewise sobriety (from Categorical Structures and their Applications), Proc. North-East Euro. Seminar, pp.265-284, World Scientific Publishing Co. Pte. Ltd (2004).